Apply mathematics (1)( a. a company’s weekly revenue r is given by the formula r = - p^2+ 30p, where p is the price of the company’s product. the company is considering hiring a distributor, which will cost the company 4p + 25 per week.

The values of price p for the product to remain profitable must be less than 1 and 25.

The value of P that will maximize the profit is 13.

For the given product to remain profitable, the revenue must continue to be greater than the cost that is R(p) > C(p)

Given the following parameters:

If R(p) > C(p), then;

Factorize to get the value of p

Hence the values of price p for the product to remain profitable must be less than 1 and 25

To maxmimize the profit, dP/dp = 0

Profit = Revenue - Cost

Profit =

Profit =

Differentiate the function and equate to zero;

Hence the value of P that will maximize the profit is 13

Learn more on cost and revenue functions here: link