Question

Given the revenue function in dollars Rx=-3x³+600x²and the cost function in dollars Cx=357x²+1800x find the marginal profit at x=10 units

Answer 1

To find the marginal profit at x=10 units, substitute x=10 into the revenue and cost functions, and subtract the cost from the revenue. The marginal profit at x=10 units is $3300.

Step-by-step explanation:

To find the marginal profit at x=10 units, we need to calculate the revenue and cost at x=10 and then subtract the cost from the revenue.

Given the revenue function Rx=-3x³+600x², we can substitute x=10 into the function to find the revenue at x=10.

R(10)=-3(10)³+600(10)² = -3(1000)+600(100) = -3000+60000 = 57000.

Similarly, substituting x=10 into the cost function Cx=357x²+1800x gives us C(10) = 357(10)²+1800(10) = 357(100)+18000 = 35700+18000 = 53700.

The marginal profit at x=10 units is the difference between the revenue and the cost at x=10:

Marginal Profit = R(10) - C(10) = 57000 - 53700 = 3300 dollars.