The company manufactures and sells x transistor radios per week. The cost of producing x radios is given by C(x)=5000+2x and the price demand equation is P = 10 - .001x where x can be no more than 10000 units.

An additional tax of $2 for each radio is introduced...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

The company manufactures and sells x transistor radios per week. The cost of producing x radios is given by C(x)=5000+2x and the price demand equation is P = 10 - .001x where x can be no more than 10000 units.

An additional tax of $2 for each radio is introduced by the government, this changes the cost function to C(x) = 5000 + 2x + 2x = 5000 + 4x

If the profit made by the company is maximized when x radios are manufactured, the total cost incurred is 5000 + 4x and the revenue is x*(10 - .001*x). The profit made is P(x) = 10x - 0.001x^2 - 5000 - 4x

= -0.001x^2 + 6x - 5000

Solve P'(x) = 0 for x

-2*0.001x + 6 = 0

=> x = 3000

**The maximum profit is $4000. The radios should be priced at $7**