A company manufactures and sells XL phones per week the weekly price demand and

Question

A company manufactures and sells XL phones per week the weekly price demand and cost equations are given below P equals 400 A company manufactures and sells xcellphones per week me weekly picedemand and cost equations are gwen below. p 400 -0.5x and cp) 15.000 140x (A) What price should the company charge for the phones. and how many phones should be produced to maximize the weekly revenue? What is the maximum wee revenue? The company should produce phones each week at a pice of s (Round to the nearest cent as needed.)

Explanation / Answer

given

p = 400 - 0.5x
p is the price per unit
revenue = quantity * price/unit
R(x) = revenue = p(x)*x = 400x - 0.5x²

p(x) maximum when first derivative is set to 0
400- 1*x = 0 ==> x = 400 quantities
price/unit : p = 400 - 0.5*400 = 400 - 200 = 200
revenue :
r(400) = 400*400 - 0.5*400²
r(2500) = 80000
The company should produce 400 phones each week at a price of $200
The maximum weekly revenue is $80000

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