Chapter 3.9, Problem 4P

To determine

To Find: The cost of manufacturing for 25 VCRs.

Answer to Problem 4P

The answer is $2650.

Explanation of Solution

Given information: Given that the manufacturing cost of different VCRs produced.

Calculation:

Let x be the number of VCRs produced and $f(x)$ be the manufacturing cost, we have $f(x)=ax+b$

First, we have to find a and b

  $\begin{array}{l}\text{Given}\text{that}\text{when}x=10,\text{we}\text{get}f(x)=1900\\ \text{so,}\text{put}\text{this}\text{values}\text{on}\text{the}\text{above}\text{equation,}\text{we}\text{have}\\ 1900=a\times 10+b\\ 1900=10a+b\\ 10a+b=1900\mathrm{...}(1)\\ \text{Similarly,}\text{when}\text{we}\text{put}x=16\text{and}f(x)=2200,\text{we}\text{have}\\ 2200=a\times 16+b\\ 2200=16a+b\\ 16a+b=2200\mathrm{...}(2)\\ \text{From}(1),\text{we}\text{get}\\ b=1900-10a\\ \text{put}\text{this}\text{value}\text{on}(2),\text{we}\text{get}\\ 16a+1900-10a=2200\\ 6a=300\\ a=50\text{and}\\ b=1900-10\times 50\\ b=1900-500\\ b=1400\end{array}$

Thus, the required linear function is $f(x)=50x+1400$

Now, the cost of manufacturing for 25 VCRs will be

  $\begin{array}{l}f(x)=50\times 25+1400\\ f(x)=1250+1400\\ f(x)=2650\end{array}$

Hence, the cost of manufacturing for 25 VCRs is $2650.