Question Tag: Optimization

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PM – Nov 2016 – L2 – Q1 – Decision Making Techniques

Evaluate profit maximization, machine bottlenecks, and inventory valuation using marginal and throughput accounting approaches.

Question

Hicenta Limited makes three products Soyi, Milco and Yoghurt. All the three
products must be offered for sale each month in order to provide a complete
market service. The products are fragile and their quality deteriorates rapidly
shortly after production.
The products are produced on two types of machine and worked on by a single
grade of direct labour. Fifty direct employees are paid N80 per hour for a
guaranteed minimum of 160 hours per month.
All the products are first pasteurised on a machine type A and then finished
and sealed on a machine type B.
The machine hour requirements for each of the products are as follows:

Machine Information:

Machine Type	Product	Hours per Unit
Machine A	Soyi	1.5
Machine A	Milco	4.5
Machine A	Yoghurt	3.0
Machine B	Soyi	1.0
Machine B	Milco	2.5
Machine B	Yoghurt	2.0

The capacity of the available machines type A and B are 6,000 hours and 5,000
hours per month respectively. Details of the selling prices, unit costs and
monthly demand for the three products are as follows:

Product Costs and Demand:

Product	Selling Price (N per unit)	Concentrate Cost (N per unit)	Other Direct Material Cost (N per unit)	Direct Labour Cost (N per unit)	Overheads (N per unit)	Profit (N per unit)	Maximum Monthly Demand (units)
Soyi	910	220	230	60	240	160	1,200
Milco	1,740	190	110	480	620	340	700
Yoghurt	1,400	160	140	360	520	220	600

Although, Hicenta Limited uses marginal costing and contribution analysis as
the basis for its decision making activities, profits are reported in the monthly
management accounts using the absorption costing basis. Finished goods
inventories are valued in the monthly management accounts at full absorption
cost.
You are required to:

a. Calculate the monthly machine utilisation rate for each product and
explain which of the machines is the bottleneck/limiting factor.
(6 Marks)
b. Use current system of marginal costing and contribution analysis to
calculate the profit maximising monthly output of the three products.
(6 Marks)
c. Explain why throughput accounting might provide more relevant
information in Hicenta‟s circumstances. (6 Marks)
d. Use a throughput approach to calculate the throughput-maximising
monthly output of the three products. (6 Marks)
e. Explain the throughput accounting approach to optimizing the level of
inventory and its valuation. Contrast this approach to the current system
employed by Hicenta. (6 Marks)

Answer

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Tags: Bottlenecks, Contribution analysis, Inventory Valuation, Marginal Costing, Optimization, Profit Maximisation, Throughput Accounting
Level: Level 2

Topic: Decision-making techniques
Series: NOV 2016

QTB – Nov 2015 – L1 – SB – Q6 – Operations Research

Formulate a linear programming problem for optimizing investment in conservative and speculative inventories under given constraints.

Question

Assume that the management of Community Bank Limited wants to invest up to N100,000 in inventory considered to be either conservative or speculative. The company’s board-approved investment policy is that the investment in conservative inventory should be at most N80,000, while the investment in the speculative inventory should be at least N12,000. Assume further that N1.6 return is expected on each naira invested in the conservative inventory, N2.0 return is expected on each investment in the speculative inventory, and that monetary policy regulations require that investment in the speculative inventory should be at most one-third of the investment in the conservative inventory.

Required:

a. State the type of Operations Research problem described above. (2 Marks)

b. Formulate mathematically the:

i. Objective function. (4 Marks)

ii. Constraint inequalities. (8 Marks)

iii. Investment problem. (6 Marks)

(Total: 20 Marks)

Answer

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Tags: Constraints, Inventory Management, Investment policy, Linear Programming, Optimization
Level: Level 1

Topic: Operations Research
Series: NOV 2015

BMF – May 2018 – L1 – SB – Q5b – Basics of Business Finance and Financial Markets

Discusses features of operational techniques in decision-making processes.

Question

State briefly the features of the following operational techniques:
i. Mathematical logic
ii. Game theory
iii. Mathematical optimisation

Answer

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Tags: Game Theory, Mathematical Logic, Operational Techniques, Optimization
Level: Level 1

Topic: Basics of Business Finance and Financial Markets
Series: MAY 2018

QT – May 2016 – L1 – Q5a – Mathematics of Business Finance

Calculate the total cost, average cost, and marginal cost of producing 5000 items, and determine the production level for the lowest average cost.

Question

a) If the total cost (in Ghana cedis) of producing $x$ items is given by the function

Required:
i) Calculate the total cost, average cost, and marginal cost of producing 5000 items. (6 marks)
ii) Determine the production level at which the average cost will be the lowest. (4 marks)

Answer

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Tags: Average Cost, Cost Functions, Marginal Cost, Optimization
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2016

QT – Nov 2017 – L1 – Q6c – Elements of Calculus

Determine the optimal production level that minimizes production costs for a company capable of producing 60,000 cans per day.

Question

If, after expanding its facilities, the company is capable of producing 60,000 cans in a day and the total daily cost is given by:

Required:
How many cans per day should they produce in order to minimize production costs?

Answer

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Tags: Derivatives, Minimization, Optimization, Production Costs
Level: Level 1

Series: NOV 2017

QT – Nov 2017 – L1 – Q6b – Elements of Calculus

Calculate marginal cost, revenue, and profit for a company’s production of beverage cans.

Question

Kyerewaa Ventures is a manufacturing company in the business of producing beverage cans for clients in the brewery industry. The weekly total cost to produce $x$ cans is given by:

The demand function for the cans is given by:

$P (x) = 200 - 0.005 x$

The company has set a production limit to 10,000 cans and it sells all the cans that are produced.

Required:
i) Derive an expression for marginal cost, marginal revenue, and marginal profit. (4 marks)
ii) Determine the cost, revenue, and profit when the 2,501st can is produced and sold. (3 marks)
iii) Determine the cost, revenue, and profit when the 7,501st can is produced and sold. (3 marks)
iv) Advise the company whether to produce the 2,501st can or the 7,501st can. (2 marks)

Answer

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Tags: Cost Function, Marginal Cost, Marginal Profit, Marginal Revenue, Optimization, Revenue Function
Level: Level 1

Series: NOV 2017

QT – May 2017 – L1 – Q1c – Basic Mathematics

Analyze the profit function to find the break-even point and number of boxes to make a profit.

Question

A paper-producing company has determined that its profit from selling $x$ hundred boxes of envelopes is given by the expression:

Required:

i) Determine the number of boxes the company must sell to break even.
(5 marks)

ii) Determine the number of boxes the company must sell to make money.
(5 marks)

Answer

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Tags: Algebra, Break-even Analysis, Optimization, Profit Function, Quadratic Equation, Quadratic Equations
Level: Level 1

Topic: Basic Mathematics
Series: MAY 2017

QT – Nov 2016 – L1 – Q2 – Linear Programming

This question involves formulating and solving a linear programming problem for maximizing profit in belt production.

Question

JinJin Company Limited makes two types of leather belts: Type Superior and Type Standard. Type Superior is of high quality, and Type Standard is of lower quality. The respective profits are GHp 40 and GHp 30 per belt. The production of each Type Superior requires twice as much time as a Type Standard belt, and if all belts were of Type Standard, the company could make 1,000 belts per day. The supply of leather is sufficient for only 800 belts per day (both types combined). Belt Type Superior requires a fancy buckle, and only 400 of these are available per day. There are only 700 buckles a day available for Type Standard.

Required:
a) Formulate this problem as a Linear Programming Model. (4 marks)

b) Set up the initial Simplex Tableau. (4 marks)

c) Solve your Tableau in (b) above. (8 marks)

d) Interpret your final Simplex Tableau. (4 marks)

Answer

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Tags: Linear Programming, Optimization, Production planning, Simplex Method
Level: Level 1

Topic: Linear Programming
Series: NOV 2016

PM – Nov 2016 – L2 – Q1 – Decision Making Techniques

Evaluate profit maximization, machine bottlenecks, and inventory valuation using marginal and throughput accounting approaches.

Question

Machine Information:

Machine Type	Product	Hours per Unit
Machine A	Soyi	1.5
Machine A	Milco	4.5
Machine A	Yoghurt	3.0
Machine B	Soyi	1.0
Machine B	Milco	2.5
Machine B	Yoghurt	2.0

Product Costs and Demand:

Product	Selling Price (N per unit)	Concentrate Cost (N per unit)	Other Direct Material Cost (N per unit)	Direct Labour Cost (N per unit)	Overheads (N per unit)	Profit (N per unit)	Maximum Monthly Demand (units)
Soyi	910	220	230	60	240	160	1,200
Milco	1,740	190	110	480	620	340	700
Yoghurt	1,400	160	140	360	520	220	600

Answer

Find Related Questions by Tags, levels, etc.

Tags: Bottlenecks, Contribution analysis, Inventory Valuation, Marginal Costing, Optimization, Profit Maximisation, Throughput Accounting
Level: Level 2

Topic: Decision-making techniques
Series: NOV 2016

QTB – Nov 2015 – L1 – SB – Q6 – Operations Research

Formulate a linear programming problem for optimizing investment in conservative and speculative inventories under given constraints.

Question

Required:

a. State the type of Operations Research problem described above. (2 Marks)

b. Formulate mathematically the:

i. Objective function. (4 Marks)

ii. Constraint inequalities. (8 Marks)

iii. Investment problem. (6 Marks)

(Total: 20 Marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Constraints, Inventory Management, Investment policy, Linear Programming, Optimization
Level: Level 1

Topic: Operations Research
Series: NOV 2015

BMF – May 2018 – L1 – SB – Q5b – Basics of Business Finance and Financial Markets

Discusses features of operational techniques in decision-making processes.

Question

State briefly the features of the following operational techniques:
i. Mathematical logic
ii. Game theory
iii. Mathematical optimisation

Answer

Find Related Questions by Tags, levels, etc.

Tags: Game Theory, Mathematical Logic, Operational Techniques, Optimization
Level: Level 1

Topic: Basics of Business Finance and Financial Markets
Series: MAY 2018

QT – May 2016 – L1 – Q5a – Mathematics of Business Finance

Calculate the total cost, average cost, and marginal cost of producing 5000 items, and determine the production level for the lowest average cost.

Question

a) If the total cost (in Ghana cedis) of producing $x$ items is given by the function

Answer

Find Related Questions by Tags, levels, etc.

Tags: Average Cost, Cost Functions, Marginal Cost, Optimization
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2016

QT – Nov 2017 – L1 – Q6c – Elements of Calculus

Determine the optimal production level that minimizes production costs for a company capable of producing 60,000 cans per day.

Question

Answer

Find Related Questions by Tags, levels, etc.

Tags: Derivatives, Minimization, Optimization, Production Costs
Level: Level 1

Series: NOV 2017

QT – Nov 2017 – L1 – Q6b – Elements of Calculus

Calculate marginal cost, revenue, and profit for a company’s production of beverage cans.

Question

Kyerewaa Ventures is a manufacturing company in the business of producing beverage cans for clients in the brewery industry. The weekly total cost to produce $x$ cans is given by:

The demand function for the cans is given by:

$P (x) = 200 - 0.005 x$

The company has set a production limit to 10,000 cans and it sells all the cans that are produced.

Answer

Find Related Questions by Tags, levels, etc.

Tags: Cost Function, Marginal Cost, Marginal Profit, Marginal Revenue, Optimization, Revenue Function
Level: Level 1

Series: NOV 2017

QT – May 2017 – L1 – Q1c – Basic Mathematics

Analyze the profit function to find the break-even point and number of boxes to make a profit.

Question

A paper-producing company has determined that its profit from selling $x$ hundred boxes of envelopes is given by the expression:

Required:

i) Determine the number of boxes the company must sell to break even.
(5 marks)

ii) Determine the number of boxes the company must sell to make money.
(5 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Algebra, Break-even Analysis, Optimization, Profit Function, Quadratic Equation, Quadratic Equations
Level: Level 1

Topic: Basic Mathematics
Series: MAY 2017

QT – Nov 2016 – L1 – Q2 – Linear Programming

This question involves formulating and solving a linear programming problem for maximizing profit in belt production.

Question

Required:
a) Formulate this problem as a Linear Programming Model. (4 marks)

b) Set up the initial Simplex Tableau. (4 marks)

c) Solve your Tableau in (b) above. (8 marks)

d) Interpret your final Simplex Tableau. (4 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Linear Programming, Optimization, Production planning, Simplex Method
Level: Level 1

Topic: Linear Programming
Series: NOV 2016

Question Tag: Optimization

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PM – Nov 2016 – L2 – Q1 – Decision Making Techniques

Evaluate profit maximization, machine bottlenecks, and inventory valuation using marginal and throughput accounting approaches.

QTB – Nov 2015 – L1 – SB – Q6 – Operations Research

Formulate a linear programming problem for optimizing investment in conservative and speculative inventories under given constraints.

BMF – May 2018 – L1 – SB – Q5b – Basics of Business Finance and Financial Markets

Discusses features of operational techniques in decision-making processes.

QT – May 2016 – L1 – Q5a – Mathematics of Business Finance

Calculate the total cost, average cost, and marginal cost of producing 5000 items, and determine the production level for the lowest average cost.

QT – Nov 2017 – L1 – Q6c – Elements of Calculus

Determine the optimal production level that minimizes production costs for a company capable of producing 60,000 cans per day.

QT – Nov 2017 – L1 – Q6b – Elements of Calculus

Calculate marginal cost, revenue, and profit for a company’s production of beverage cans.

QT – May 2017 – L1 – Q1c – Basic Mathematics

Analyze the profit function to find the break-even point and number of boxes to make a profit.

QT – Nov 2016 – L1 – Q2 – Linear Programming

This question involves formulating and solving a linear programming problem for maximizing profit in belt production.

PM – Nov 2016 – L2 – Q1 – Decision Making Techniques

Evaluate profit maximization, machine bottlenecks, and inventory valuation using marginal and throughput accounting approaches.

QTB – Nov 2015 – L1 – SB – Q6 – Operations Research

Formulate a linear programming problem for optimizing investment in conservative and speculative inventories under given constraints.

BMF – May 2018 – L1 – SB – Q5b – Basics of Business Finance and Financial Markets

Discusses features of operational techniques in decision-making processes.

QT – May 2016 – L1 – Q5a – Mathematics of Business Finance

Calculate the total cost, average cost, and marginal cost of producing 5000 items, and determine the production level for the lowest average cost.

QT – Nov 2017 – L1 – Q6c – Elements of Calculus

Determine the optimal production level that minimizes production costs for a company capable of producing 60,000 cans per day.

QT – Nov 2017 – L1 – Q6b – Elements of Calculus

Calculate marginal cost, revenue, and profit for a company’s production of beverage cans.

QT – May 2017 – L1 – Q1c – Basic Mathematics

Analyze the profit function to find the break-even point and number of boxes to make a profit.

QT – Nov 2016 – L1 – Q2 – Linear Programming

This question involves formulating and solving a linear programming problem for maximizing profit in belt production.

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