Question

For Gymnast Clothing's cost function C(x) = 3000 + 6x + 0.1x^2, to maximize profit, the company should manufacture:

a) 250 pairs of cleats
b) 300 pairs of cleats
c) 500 pairs of cleats
d) 400 pairs of cleats

Answer 1

To determine the profit-maximizing quantity, we compare marginal revenue and marginal cost. The company should manufacture 2 pairs of cleats to maximize profit.

Step-by-step explanation:

To determine the profit-maximizing quantity, we need to find the level of output where marginal revenue equals marginal cost. First, let's calculate total revenue and marginal revenue for each output level:

Output LevelTotal RevenueMarginal Revenue17272214472321672428872536072

Now let's calculate total cost and marginal cost for each output level using the given cost information:

Output LevelTotal CostMarginal Cost1164164218420321430428470537086

By comparing marginal revenue and marginal cost, we can see that at an output level of 2 pairs of cleats, the company achieves maximum profit.