Topic: Elements of Calculus

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

Distinguish between marginal cost and average cost in production.

Question

Distinguish between marginal cost and average cost in production.

Answer

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Tags: Average Cost, Marginal Cost, Production Costs
Level: Level 1

Topic: Elements of Calculus

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

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

Question

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)

Answer

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Tags: Fixed Cost, Integration, Marginal Cost, Total Cost
Level: Level 1

Topic: Elements of Calculus
Series: MAY 2017

QT – May 2017 – L1 – Q3a – Elements of Calculus

Differentiate a cost function and determine how quickly the cost is changing at a specific production level.

Question

The AXM manufacturing company has determined that the cost function for producing a particular type of pavement block is given by:

Where $x$ is measured in number of units and $C (x)$ in GH¢.

Required:

i) Calculate the derivative of $C (x)$ with respect to $x$ .
(5 marks)

ii) Determine how quickly the cost is changing at
(4 marks)

Answer

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Tags: Cost Function, Differentiation, Rate of Change
Level: Level 1

Topic: Elements of Calculus
Series: MAY 2017

QT – Nov 2016 – L1 – Q6b – Elements of Calculus

Calculate the number of tons of low and high-grade steel to produce to maximize total revenue and determine the maximum total revenue.

Question

Tema Steel Plant is capable of producing tons per day of low-grade steel and tons per day of high-grade steel, where:

If the fixed market price of low-grade steel is GH¢6.90 and the fixed market price of high-grade steel is GH¢13.80:

i) Determine the number of tons of low-grade steel and high-grade steel to be produced to maximize total revenue. (10 marks)

ii) Determine the maximum total revenue. (4 marks)

Answer

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Tags: Calculus, Production, Revenue Maximization, Steel Plant
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2016

QT – Nov 2016 – L1 – Q6a – Elements of Calculus

Sketch the critical points on a cost or revenue function, including maximum, minimum, and inflexion points.

Question

Sketch Graph(s) to show the following critical points on a cost or revenue function:

i) Local Maximum Point (1 mark)
ii) Absolute Maximum Point (1 mark)
iii) Local Minimum Point (1 mark)
iv) Absolute Minimum Point (1 mark)
v) Point of inflexion (2 marks)

Answer

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Tags: Graph Sketching, Inflexion Point, Maximum Point, Minimum Point, Revenue Functio
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2016

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.

Question

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

The marginal cost function is given by:

Let 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)

Answer

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Tags: Integration, Marginal Cost, Marginal Revenue, Total Profit, Total Revenue
Level: Level 1

Topic: Elements of Calculus
Series: MAY 2018

QT – Nov 2018 – L1 – Q2c – Elements of Calculus

Determine and interpret the elasticity of demand at different price levels for kente strips.

Question

Due to changes in market conditions, the company finds the demand $q$ (in thousands) for their kente strips to be of GH¢ per kente strip.

Required:
(i) Determine the elasticity of demand when the price is GH¢5 and when the price is GH¢15 per kente strip. (6 marks)
(ii) Comment on your results in (i). (2 marks)

Answer

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Tags: Demand Function, Elasticity of Demand, Market conditions, Price
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2018

QT – Nov 2018 – L1 – Q2b – Elements of Calculus

Determine the price and quantity that maximize revenue and profit, and compute the maximum profit for Renes Trading Company.

Question

Renes Trading Company sells $q$ kente strips per month at $p$ Ghana Cedis per kente strip. The demand function for kente strips is given by $p = 300 - 0.02 q$ . The kente strips cost GH¢30 per strip to manufacture. There are fixed costs of GH¢9,000 per month.

Required:
(i) Determine the price per kente strip that will maximize revenue. (4 marks)
(ii) Determine the quantity where profit is maximized. (4 marks)
(iii) Calculate the maximum profit. (2 marks)

Answer

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Tags: Differentiation, Elasticity of Demand, Profit Maximization, Revenue Maximization
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2018

QT – Nov 2018 – L1 – Q2a – Elements of Calculus

Define the stationary point of a differentiable function of one variable.

Question

What is a Stationary Point of a differentiable function of one variable?

Answer

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Tags: Differentiation, Maximum and Minimum, Stationary Point
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2018

QT – Nov 2015 – L1 – Q7b – Elements of Calculus

Determine the number of TV sets a manufacturer should produce to maximize profit and calculate the maximum profit.

Question

A TV manufacturer finds that he can sell $x$ units per week at a price $p = 250 - 0.5 x$ each. His cost of production of $x$ TV sets per week is given by $C = 240 + 2 x$ .

Required:
(i) Determine how many sets per week he should produce to maximize his profit. (5 Marks)
(ii) Determine the maximum profit. (2 Marks)

Answer

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Tags: Marginal Cost, Marginal Revenue, Production, Profit Maximization, TV Sets
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2015

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

Distinguish between marginal cost and average cost in production.

Question

Distinguish between marginal cost and average cost in production.

Answer

Find Related Questions by Tags, levels, etc.

Tags: Average Cost, Marginal Cost, Production Costs
Level: Level 1

Topic: Elements of Calculus

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

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

Question

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)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Fixed Cost, Integration, Marginal Cost, Total Cost
Level: Level 1

Topic: Elements of Calculus
Series: MAY 2017

QT – May 2017 – L1 – Q3a – Elements of Calculus

Differentiate a cost function and determine how quickly the cost is changing at a specific production level.

Question

The AXM manufacturing company has determined that the cost function for producing a particular type of pavement block is given by:

Where $x$ is measured in number of units and $C (x)$ in GH¢.

Required:

i) Calculate the derivative of $C (x)$ with respect to $x$ .
(5 marks)

ii) Determine how quickly the cost is changing at
(4 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Cost Function, Differentiation, Rate of Change
Level: Level 1

Topic: Elements of Calculus
Series: MAY 2017

QT – Nov 2016 – L1 – Q6b – Elements of Calculus

Calculate the number of tons of low and high-grade steel to produce to maximize total revenue and determine the maximum total revenue.

Question

Tema Steel Plant is capable of producing tons per day of low-grade steel and tons per day of high-grade steel, where:

If the fixed market price of low-grade steel is GH¢6.90 and the fixed market price of high-grade steel is GH¢13.80:

i) Determine the number of tons of low-grade steel and high-grade steel to be produced to maximize total revenue. (10 marks)

ii) Determine the maximum total revenue. (4 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Calculus, Production, Revenue Maximization, Steel Plant
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2016

QT – Nov 2016 – L1 – Q6a – Elements of Calculus

Sketch the critical points on a cost or revenue function, including maximum, minimum, and inflexion points.

Question

Sketch Graph(s) to show the following critical points on a cost or revenue function:

i) Local Maximum Point (1 mark)
ii) Absolute Maximum Point (1 mark)
iii) Local Minimum Point (1 mark)
iv) Absolute Minimum Point (1 mark)
v) Point of inflexion (2 marks)

Answer

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Tags: Graph Sketching, Inflexion Point, Maximum Point, Minimum Point, Revenue Functio
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2016

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.

Question

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

The marginal cost function is given by:

Let be the number of items either produced or sold.

Answer

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Tags: Integration, Marginal Cost, Marginal Revenue, Total Profit, Total Revenue
Level: Level 1

Topic: Elements of Calculus
Series: MAY 2018

QT – Nov 2018 – L1 – Q2c – Elements of Calculus

Determine and interpret the elasticity of demand at different price levels for kente strips.

Question

Due to changes in market conditions, the company finds the demand $q$ (in thousands) for their kente strips to be of GH¢ per kente strip.

Required:
(i) Determine the elasticity of demand when the price is GH¢5 and when the price is GH¢15 per kente strip. (6 marks)
(ii) Comment on your results in (i). (2 marks)

Answer

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Tags: Demand Function, Elasticity of Demand, Market conditions, Price
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2018

QT – Nov 2018 – L1 – Q2b – Elements of Calculus

Determine the price and quantity that maximize revenue and profit, and compute the maximum profit for Renes Trading Company.

Question

Answer

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Tags: Differentiation, Elasticity of Demand, Profit Maximization, Revenue Maximization
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2018

QT – Nov 2018 – L1 – Q2a – Elements of Calculus

Define the stationary point of a differentiable function of one variable.

Question

What is a Stationary Point of a differentiable function of one variable?

Answer

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Tags: Differentiation, Maximum and Minimum, Stationary Point
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2018

QT – Nov 2015 – L1 – Q7b – Elements of Calculus

Determine the number of TV sets a manufacturer should produce to maximize profit and calculate the maximum profit.

Question

A TV manufacturer finds that he can sell $x$ units per week at a price $p = 250 - 0.5 x$ each. His cost of production of $x$ TV sets per week is given by $C = 240 + 2 x$ .

Required:
(i) Determine how many sets per week he should produce to maximize his profit. (5 Marks)
(ii) Determine the maximum profit. (2 Marks)

Answer

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Tags: Marginal Cost, Marginal Revenue, Production, Profit Maximization, TV Sets
Level: Level 1