Question Tag: Revenue Maximization

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QMDDM – OCT 2022 – L2 – Q4 – Revenue Cost Profit Optimization

Given total revenue TR = -14x² + 2000x and total cost TC = x³ - 15x² + 1000 functions, explain marginal and average concepts, and calculate production levels to maximize revenue, minimize cost, maximize profit, with comments.

The total revenue and total cost for a product are related to production x by:

2 14 2000 TR X X

− +

3 2 15 1000 TC X X

− +

(a) Explain briefly (in your own words) the following terms in relation to the total revenue

and total cost above: (i) Marginal Cost (ii) Marginal Revenue (iii) Marginal Profit (iv) Average Revenue

(b) Calculate, how many units should the company produce in order to

(i) Maximize total revenue (ii) Minimize cost (iii) Maximize profit. (iv) Comment on (i), (ii) and (iii) above.

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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.

Tema Steel Plant is capable of producing q1 tons per day of low-grade steel and q2 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)

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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.

Renes Trading Company sells qq kente strips per month at pp Ghana Cedis per kente strip. The demand function for kente strips is given by p=300−0.02qp = 300 – 0.02q. 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)

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QMDDM – OCT 2022 – L2 – Q4 – Revenue Cost Profit Optimization

Given total revenue TR = -14x² + 2000x and total cost TC = x³ - 15x² + 1000 functions, explain marginal and average concepts, and calculate production levels to maximize revenue, minimize cost, maximize profit, with comments.

The total revenue and total cost for a product are related to production x by:

2 14 2000 TR X X

− +

3 2 15 1000 TC X X

− +

(a) Explain briefly (in your own words) the following terms in relation to the total revenue

and total cost above: (i) Marginal Cost (ii) Marginal Revenue (iii) Marginal Profit (iv) Average Revenue

(b) Calculate, how many units should the company produce in order to

(i) Maximize total revenue (ii) Minimize cost (iii) Maximize profit. (iv) Comment on (i), (ii) and (iii) above.

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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.

Tema Steel Plant is capable of producing q1 tons per day of low-grade steel and q2 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)

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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.

Renes Trading Company sells qq kente strips per month at pp Ghana Cedis per kente strip. The demand function for kente strips is given by p=300−0.02qp = 300 – 0.02q. 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)

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