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Chapter 5: Q. 67 (page 257)

The number Nof cars produced at a certain factory in one day after thours of operation is given by N(t)=100t-5t2,0鈮�t鈮�10.If the cost C(in dollars) of producing N cars is C(N)=15,000+8000N,find the cost Cas a function of the time tof operation of the factory.

Short Answer

Expert verified

Hence,C(t)=15,000+8,00,000t-40,000t2.

Step by step solution

01

Step 1. Given Information

Given that N(t)=100t-5t2,0鈮�t鈮�10andC(N)=15,000+8000N.

02

Step 2. Solution

We have to find the cost Cas a function of time tthat is we have to find C鈭�N(t).

Here, C(N)=15,000+8000Nand N(t)=100t-5t2.

So,

C鈭�N(t)=C(N(t))C鈭�N(t)=15,000+8000(N(t))C鈭�N(t)=15000+8000{100t-5t2}C鈭�N(t)=15,000+8,00,000t-40,000t2C(t)=15,000+8,00,000t-40,000t2.

03

Step 3. Final Answer

Hence, C as a function of time tis: -

C(t)=15,000+8,00,000t-40,000t2.

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