2. The sale department of Company A has found that selling price per uni has the

Question

2. The sale department of Company A has found that selling price per uni has the following relationship with number of units sold per year: P $55.00 0.05Q where P-selling price per unit 2 - quantity sold per year On the other hand, the management of Company A has found that the cost of g has the following relation ship with the number of units sold per year: C $6.00Q+ $9800 where C-cost to produce and sell Q per year What quantity should the company produce and sell each year to gain the maximum profit? (25 pts)

Explanation / Answer

Answer 2

Profit Maximizing Condition

In order to maximize Profit a company should produce that amount at which Marginal Revenue(MR) = Marginal Cost(MC)

MR = d(TR)/dQ = d(P*Q)/dQ = d(55Q - 0.05Q2)/dQ = 55 - 0.1Q

MC = dC/dQ = 6

Hence 55 - 0.1Q = 6 => Q = 490

Hence A company should produce and 490 units in order to mazimize Profit.

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