Question Tag: Marginal Cost

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QTB – May 2016 – L1 – SB – Q5a – Mathematics

This question involves finding the total cost function and the cost of producing 50 items using marginal cost and integration.

The marginal cost of producing a particular item is given by

Required:
i. Find the total cost function C(q), if the cost of producing 2 items is N1,660.
(7 marks)

ii. Find the cost of producing 50 items.

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

This question involves calculating the change in revenue, total revenue, total cost, and total profit for a manufacturer based on given marginal cost and marginal revenue functions.

A manufacturer determines that the firm’s Marginal Cost (MC) and Marginal Revenue (MR) functions are:

MC=C′(x) = 100 − 0.1x

MR = R(x)=100 + 0.1x

You are required to find the:

a. Change in revenue that results when the sales level increases from 20 to 30 units. (5 Marks)
b. Revenue resulting from the sale of 30 units. (5 Marks)
c. Cost of producing 30 units if the fixed cost (at x=0x = 0) is N400. (5 Marks)
d. Total profit when 30 units of the product are sold. (5 Marks)

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QTB – Nov 2015 – L1 – SA – Q7 – Operations Research

This question identifies which factor does not affect the optimal replacement interval for an asset.

If an asset can be replaced at the same cost and there is no time value of money, then the problem of obtaining the optimal replacement interval involves the following EXCEPT:

A. Finding the cumulative operating/maintenance cost
B. Finding the total depreciation
C. Adding (A) and (B) above to get total cost
D. Finding the year at which marginal cost is minimized
E. Finding the year at which average cost is minimum

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PM – May 2019 – L2 – Q7 – Pricing Decisions

Evaluates various pricing methods for a new product and calculates prices based on different strategies.

Tetpack Nigerian Limited (TNL) produces various types of packaging products for the food industry. TNL has just introduced a new type of pack, and its marketing manager is considering how to penetrate the market with the pack. The following pricing strategies have been suggested:

i. Market skimming price
ii. Market penetration price
iii. Full cost plus price
iv. Return on investment price
v. Marginal cost plus price

The management accountant has provided the following data about the pack:

  • Non-current assets needed for the production of the pack: N2,000,000
  • Working capital requirements: N400,000
  • Expected annual sales volume: 40,000 units
  • Variable production costs: N60 per unit
  • Fixed production costs: N300,000 each year
  • Annual non-production costs: N100,000
  • Markup:
    • Full cost plus price: 25%
    • Marginal cost plus price: 40%
    • Target return on investment: 10% per year

Required:
a. Discuss the above pricing methods and advise when each could be used. (10 Marks)

b. Calculate what the price of the pack should be if its price is based on:
i. Full cost plus pricing (1½ Marks)
ii. Marginal cost plus pricing (1½ Marks)
iii. Return on investment pricing (2 Marks)

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MI – May 2016 – L1 – SA – Q11 – Cost-Volume-Profit Analysis

Calculate the number of units required to break even given the fixed costs, sales price, and marginal cost.

A company manufactures a single product with a sales price of N1,000 and a marginal cost of N650. If the fixed cost is N685,300 per annum, then the number of units required to Break Even is:

A. 1,950
B. 1,955
C. 1,958
D. 1,985
E. 1,988

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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.

a) If the total cost (in Ghana cedis) of producing xx items is given by the function C (x) = 2600 + 2x +

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)

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

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

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:

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)

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QT – Nov 2017 – L1 – Q6a – Elements of Calculus

Distinguish between marginal cost and average cost in production.

Distinguish between marginal cost and average cost in production.

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QT – May 2017 – L1 – Q3b – Elements of Calculus

Use integration to calculate total cost from a marginal cost function with a given fixed cost.

At the Zee manufacturing company, the marginal cost for producing x gears, measured in hundreds, is:

If the fixed cost (the cost of producing zero items) is GH¢3000:

Required:

Determine the total cost for manufacturing 5000 gears.
(11 marks)

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QT – May 2018 – L1 – Q3 – Elements of Calculus

Calculate total revenue, items for maximum revenue, and total profit from given marginal revenue and cost functions.

a) The marginal revenue function of a manufacturing company is given by:

The marginal cost function is given by:

Let x be the number of items either produced or sold.

Required:
i) Calculate the revenue generated when 50 items are sold. (2 marks)
ii) Calculate the number of items that will yield maximum revenue. (4 marks)
iii) Calculate the total revenue if 100 items are produced. (4 marks)
iv) Calculate the total profit for the 100 items. (4 marks)
v) If a tax of 20% is imposed on each item produced, find the cost of 100 items. (6 marks)

 

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QTB – May 2016 – L1 – SB – Q5a – Mathematics

This question involves finding the total cost function and the cost of producing 50 items using marginal cost and integration.

The marginal cost of producing a particular item is given by

Required:
i. Find the total cost function C(q), if the cost of producing 2 items is N1,660.
(7 marks)

ii. Find the cost of producing 50 items.

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

This question involves calculating the change in revenue, total revenue, total cost, and total profit for a manufacturer based on given marginal cost and marginal revenue functions.

A manufacturer determines that the firm’s Marginal Cost (MC) and Marginal Revenue (MR) functions are:

MC=C′(x) = 100 − 0.1x

MR = R(x)=100 + 0.1x

You are required to find the:

a. Change in revenue that results when the sales level increases from 20 to 30 units. (5 Marks)
b. Revenue resulting from the sale of 30 units. (5 Marks)
c. Cost of producing 30 units if the fixed cost (at x=0x = 0) is N400. (5 Marks)
d. Total profit when 30 units of the product are sold. (5 Marks)

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QTB – Nov 2015 – L1 – SA – Q7 – Operations Research

This question identifies which factor does not affect the optimal replacement interval for an asset.

If an asset can be replaced at the same cost and there is no time value of money, then the problem of obtaining the optimal replacement interval involves the following EXCEPT:

A. Finding the cumulative operating/maintenance cost
B. Finding the total depreciation
C. Adding (A) and (B) above to get total cost
D. Finding the year at which marginal cost is minimized
E. Finding the year at which average cost is minimum

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PM – May 2019 – L2 – Q7 – Pricing Decisions

Evaluates various pricing methods for a new product and calculates prices based on different strategies.

Tetpack Nigerian Limited (TNL) produces various types of packaging products for the food industry. TNL has just introduced a new type of pack, and its marketing manager is considering how to penetrate the market with the pack. The following pricing strategies have been suggested:

i. Market skimming price
ii. Market penetration price
iii. Full cost plus price
iv. Return on investment price
v. Marginal cost plus price

The management accountant has provided the following data about the pack:

  • Non-current assets needed for the production of the pack: N2,000,000
  • Working capital requirements: N400,000
  • Expected annual sales volume: 40,000 units
  • Variable production costs: N60 per unit
  • Fixed production costs: N300,000 each year
  • Annual non-production costs: N100,000
  • Markup:
    • Full cost plus price: 25%
    • Marginal cost plus price: 40%
    • Target return on investment: 10% per year

Required:
a. Discuss the above pricing methods and advise when each could be used. (10 Marks)

b. Calculate what the price of the pack should be if its price is based on:
i. Full cost plus pricing (1½ Marks)
ii. Marginal cost plus pricing (1½ Marks)
iii. Return on investment pricing (2 Marks)

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MI – May 2016 – L1 – SA – Q11 – Cost-Volume-Profit Analysis

Calculate the number of units required to break even given the fixed costs, sales price, and marginal cost.

A company manufactures a single product with a sales price of N1,000 and a marginal cost of N650. If the fixed cost is N685,300 per annum, then the number of units required to Break Even is:

A. 1,950
B. 1,955
C. 1,958
D. 1,985
E. 1,988

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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.

a) If the total cost (in Ghana cedis) of producing xx items is given by the function C (x) = 2600 + 2x +

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)

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

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

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:

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)

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QT – Nov 2017 – L1 – Q6a – Elements of Calculus

Distinguish between marginal cost and average cost in production.

Distinguish between marginal cost and average cost in production.

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QT – May 2017 – L1 – Q3b – Elements of Calculus

Use integration to calculate total cost from a marginal cost function with a given fixed cost.

At the Zee manufacturing company, the marginal cost for producing x gears, measured in hundreds, is:

If the fixed cost (the cost of producing zero items) is GH¢3000:

Required:

Determine the total cost for manufacturing 5000 gears.
(11 marks)

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QT – May 2018 – L1 – Q3 – Elements of Calculus

Calculate total revenue, items for maximum revenue, and total profit from given marginal revenue and cost functions.

a) The marginal revenue function of a manufacturing company is given by:

The marginal cost function is given by:

Let x be the number of items either produced or sold.

Required:
i) Calculate the revenue generated when 50 items are sold. (2 marks)
ii) Calculate the number of items that will yield maximum revenue. (4 marks)
iii) Calculate the total revenue if 100 items are produced. (4 marks)
iv) Calculate the total profit for the 100 items. (4 marks)
v) If a tax of 20% is imposed on each item produced, find the cost of 100 items. (6 marks)

 

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