Question

The marginal revenue R=296 - 4q and

marginal cost is 72 with fixed cost 2,000.
Find the price that will maximize profit.

Answer 1

To find the price that will maximize profit, set the marginal revenue equal to the marginal cost, solve for the quantity, and substitute it back into the marginal revenue equation to find the corresponding price. In this case, the price that will maximize profit is $72.

Step-by-step explanation:

To find the price that will maximize profit, we need to find the quantity that maximizes the difference between marginal revenue and marginal cost. Marginal revenue (MR) is the additional revenue gained from selling one more unit, and marginal cost (MC) is the additional cost incurred from producing one more unit.

1. First, set MR equal to MC:
2. 296 - 4q = 72
3. Solve for q:
4. 4q = 296 - 72
5. 4q = 224
6. q = 56
7. Substitute the value of q back into the marginal revenue equation to find the corresponding price:
8. R = 296 - 4(56)
9. R = 296 - 224
10. R = $72

Therefore, the price that will maximize profit is $72.