If Slick Shades has a constant marginal cost of production equal to $40 and the distributors have a constant marginal cost of distribution equal to $20, what is the profit- maximizing number of sunglasses (in hundreds)for Slick Shades to produce?
A)50
B)80
C)70
D)90

Question

Quizplus · Accepted Answer

To maximize profit, Slick Shades should produce where marginal cost equals marginal revenue. Since the question only provides information on the marginal cost and not the demand, we cannot find the exact marginal revenue. However, we can use the fact that profit is maximized where marginal cost equals marginal revenue to find the optimal quantity of production.

Let Q be the quantity produced in hundreds. Then, the total cost of production is:
Total Cost = 40Q

The cost to distribute each pair of sunglasses is $20, so the total cost of distribution is:
Total Distribution Cost = 20Q

The total cost of production and distribution is:
Total Cost = 40Q + 20Q = 60Q

Assuming there are no fixed costs, the profit equation is:
Profit = Revenue - Total Cost

To find the profit-maximizing quantity, we need to set the derivative of profit with respect to Q equal to zero:
dProfit/dQ = 0

Since we don't know the price or demand, we can't differentiate the revenue function, but we can assume that marginal revenue is positive. Therefore, we can assume that the profit-maximizing quantity is where marginal cost equals marginal revenue.

Marginal Cost = Total Cost' = 60
Marginal Revenue = Price' + (Quantity Sold)' * ((Price') / (Quantity Sold)') = Price'

40 = Price'
Price = 40

Therefore, the profit-maximizing quantity is:
Marginal Cost = Marginal Revenue
40 = Price
40 = 40
60Q = 40Q * 40
Q = 80

So Slick Shades should produce 80 hundred sunglasses to maximize profit. Answer: B

If Slick Shades Has a Constant Marginal Cost of Production