Chapter 4.8, Problem 22P

To determine

To find how many calculators per day can it manufacture ?

Answer to Problem 22P

300 calculators per day it manufacture .

Explanation of Solution

Given information: Equation, $C=n\left(20-0.01n\right)+100$ . The size of the plant limits the maximum output to 500 calculators per day.The company plans to invest $5200 per day in manufacturing cost.

Calculation: The required solution is obtained as,

The given equation is , $C=n\left(20-0.01n\right)+100$

  $\begin{array}{l}C=n\left(20-0.01n\right)+100\\ 5200=20n-0.01n^2+100\\ 0.01n^2-20n+5100=0\\ n^2-2000n+510000=0\\ \left(n-1700\right)\left(n-300\right)=0\\ n=1700,300\end{array}$

1700 is too large a number (maximum output is 500 calculator per day)

  $n=300$

Hence, 300 calculators per day it manufacture .