- 25 Marks
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.
Question
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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