A company manufactures and sells x cellphones per week. The weekly price-demand

Question

A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below. p-500-0.5x and -25.000. 130 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 weekly revenue The company should produce phones each week at a price of Round to the nearest cent as needed.) Example of what answer should look like A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below p J 400 -0.1x and CX) S 15.000 135x (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 weekly revenue The company should produce 2,000 phones each week at a price of s 200 Round to the nearest cent as needed.) The maximum weekly revenue is 400,000.00. (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce 1,325 phones each week at a price of 267.50 Round to the nearest cent as needed.) The maximum weekly profit is 160,562.50 (Round to the nearest cent as needed

Explanation / Answer

p = 500 - 0.5x

x cellphones are sold

So, R(x) = x(500 - 0.5x) = -0.5x^2 + 500x

C(x) = 25000 + 130x

A) R'(x) = -1x + 500 = 0

1x = 500

x = 500

p = 500 - 0.5x = 500 - 0.5(500) = 500 - 250 = 250

So, "the company should produce 500 phones each week at a price of 250 ----> ANSWER

R(500) = -0.5x^2 + 500x = -0.5(500)^2 + 500(500) = 125000

The max weekly revenue = 125000 ---> ANSWER

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B)

Profit = R - C

P(x) = -0.5x^2 + 500x - (25000 + 130x)

P(x) = -0.5x^2 + 370x - 25000

P'(x) = -1x + 370 = 0 ---> x = 370

p = 500 - 0.5(370) = 315

So, "the company should produce 370 phones each week at a price of 315" ----> ANSWER

P(x) = -0.5x^2 + 370x - 25000

P(370) = -0.5(370)^2 + 370(370) - 25000 = 43450

The max weekly profit = 43450 ---> ANSWER

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