company manufactures and sells x cellphones per week. The weekly pr equations ar
ID: 2885617 • Letter: C
Question
company manufactures and sells x cellphones per week. The weekly pr equations are given below. p 400-0.1x and C(x) 25,000+135x A. Find the weekly revenue function. B. How many phones should be produced to maximize the weekly revenue? C. What price should the company charge for the phones? D. What is the weekly revenue? E. Find the weekly profit function. F. How many phones should be produced to maximize the weekly profit? G. What price should the company charge for the phones? H. What is the weekly profit?Explanation / Answer
2)
p= 400-0.1x ,C(x)=25000+135x
A)
weekly revenue function, R(x)=x p(x)
=>R(x)=x(400-0.1x)
=>R(x)=(400x-0.1x2)
B)
R(x)=-0.1(x2-4000x)
=>R(x)=-0.1(x2?-4000x+20002-20002)
=>R(x)=-0.1(x2?-4000x+20002)+(0.1*20002)
=>R(x)=-0.1(x-2000)2+(400000)
2000 phones should be produced to maximise the weekly revenue
C)
p=400-(0.1*2000)
=>p=400-200
=>p=200
company should charge price of 200 for each phone
D)
weekly revenue =400x-0.1x2
maximum weekly revenue =400000
E)
weekly profit,P(x)=R(x)-C(x)
=>P(x)=(400x-0.1x2)-(25000+135x)
=>P(x)=400x-0.1x2-25000-135x
=>P(x)=-0.1x2+265x-25000
F)
P(x)=-0.1(x2-2650x)-25000
=>P(x)=-0.1(x2-2650x+13252-13252)-25000
=>P(x)=-0.1(x2-2650x+13252)+(0.1*13252)-25000
=>P(x)=-0.1(x-1325)2+150562.5
1325 phones should be produced for the maximum profit
G)
p=400-(0.1*1325)
=>p=267.5
company should charge price of 267.5 for each phone
H)
weekly profit=-0.1x2+265x-25000
maximum weekly profit =150562.5
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