Question

he weekly revenue for a product is given by R(x)=102.6x-0.015x^(2), and the weekly cost is (x)=9000+51.3x-0.03x^(2)+0.00001x^(3), where x is the number of units produced and sold.

Answer 1

To obtain the profit from selling x items, we have to subtract the cost of production, C(x) from the revenue received from selling those units, R(x). Hence, the profit function P(x) is given by:

P(x) = R(x) - C(x) = [102.6x - 0.015x^2] - [9000 + 51.3x - 0.03x^2 + 0.00001x^3]

To calculate the profit for a certain number of items, just substitute that value as x in profit function.

For example, if you wish to compute the profit for 500 units:
Set x = 500 and substitute it in the profit equation, P(500).
So,
P(500) = [102.6*(500) - 0.015*(500^2)] - [9000 + 51.3*(500) - 0.03*(500^2) + 0.00001*(500^3)]

Performing all the operations we will obtain the value of profit for 500 units produced and sold. This approach can be used to evaluate the profit for any given number of units.