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Chapter 5: Q. 70 (page 258)

The price p, in dollars, of a certain commodity and the quantity xsold obey the demand equation p=-15x+200,0鈮�x鈮�1000.Suppose that the cost C, in dollars, of producing xunits is C=x10+400.

Assuming that all items produced are sold, find the cost C as a function of the price p.

Short Answer

Expert verified

The cost function, C(p)=-5p+100010+400.

Step by step solution

01

Step 1. Given Information

Given thatp(x)=-15x+200,0鈮�x鈮�1000,andC(x)=x10+400.

02

Step 2. Solution

Here, p(x)=-15x+200,0鈮�x鈮�1000and C(x)=x10+400.

We have to find the cost Cas a function of p.

Now,

p=-15x+200,0鈮�x鈮�1000p-200=-15x5(p-200)=-xx(p)=-5p+1000,0鈮�p鈮�200.

C as a function of price p is C鈭�x(p).

So,

C鈭�x(p)=C(x(p))C鈭�x(p)=x(p)10+400C鈭�x(p)=-5p+100010+400C(p)=-5p+100010+400

03

Step 3. Final answer

Hence,C(p)=-5p+100010+400.

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