Q32. - 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.

32. Draw the graph showing the feasible region.

Step-by-Step Solution

Answer

The graph of respective inequalities is,

Step-1 –Finding the corner point

Given inequalities are $1\frac{1}{2}g+c\le 85;2g+\frac{c}{2}\le 40;x,y\ge 0$

Their respective linear equations are  $\frac{3}{2}g+c=85;2g+\frac{c}{2}=40;x,y=0$

The point which satisfies the equation $\frac{3}{2}g+c=85$  are  $(0,85)and(\frac{170}{3},0)$

And $2g+\frac{c}{2}=40$ are$(20,0)$   and  $(0,80)$

Step-2 –Plot the corner points and determine the feasible region

We choose the point $(0,0)$ to obtain the shaded region.

The point $(0,0)$ satisfies the inequalities

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

So, the graph of respective inequalities are