Q31. - Algebra 2

Question

There are a total of   workers hours available per day for production at a calculator manufacturer. There are   workers hours variable for encasement and Quality Control each day. The table below shows the number of hours needed in each department for two different types of Calculators.

31. Let g represent the number of graphing calculators and let c represent the number of CAS calculator. Write a system of inequalities to represent the number of calculators than can be produced.

Step-by-Step Solution

Answer

The systems of inequalities are $\begin{array}{c}1\frac{1}{2}g+c\le 85;2g+\frac{1}{2}c\le 40;\\ x,y\ge 0\end{array}$

Step-1 –Assumption of variable

Let g represent the number of graphing calculator.

Let c represent the number of CAS calculator.

Step-2 –Determination of Inequalities

Total workers hours available per day for production= 85

Total workers hours available for encasement and Quality control= 40

 1 graphing calculator takes $1\frac{1}{2}$  hour’s production time

1  CAS takes 1  hour production time

And,

1  graphing calculator take 2  hours Encasement and Quality control

1  CAS take $\frac{1}{2}$  hours in Encasement and Quality control

So,$\begin{array}{c}1\frac{1}{2}g+c\le 85\\ 2g+\frac{1}{2}c\le 40\\ andg,c\ge 0\end{array}$