Suppose that the demand for refrigerated juice is given by the following functio

Question

Suppose that the demand for refrigerated juice is given by the following function: P = 160 – 4Q. The cost per unit of production of refrigerated juice is described by C = 10 – 0.25Q. If the producers in this industry are trying to determine the optimal production quantity, what would be your advice to them? Please provide a mathematical argument and show that the production level you suggest corresponds to profit maximization. (Hint: use derivative of whatever function you are trying to maximize and set it equal to zero). Profit = TR-TC

Explanation / Answer

Demand Function = P = 160 – 4Q.

Cost Function = C = 10 – 0.25Q

Optimal quantity of production is the quantity at which total cost is equal to total revenue. This quantity is also called breakeven quantity.

160 – 4Q = 10 – 0.25Q

150 = 3.75Q

Q = 40 unit

So optimal quantity of production is 40 unit. Company will earn profit when it produce more than 40 unit.

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