I seem to be having problems setting up Linear Programming questions.

Question

For example:

Kustom Kars does van conversions. The Custom conversion required 15 hours of shop time, 8 hours of painting time, and 1 hour of inspection time. The Deluxe conversion requires 12 hours of conversion time, 12 hours of painting time, and 1.5 hours of inspection time. There are 90 hours of shop time, 72 hours of painting time, and 10 hours of inspection time in the coming two weeks. How many conversion of each type should Kustom Kars peform assuming that each Custom conversion results in $175 profit and each Deluxe conversion results in $225 profit? What's the Max profit?

I keep thinking that there are 3 variables (shop, paint, & inspection time) and am unable to graph any lines. So far this is how I've set this problem up:

X= number of Custom Conversions
Y= number of Deluxe Conversions
Max(P)=$175X + $225Y

X=15shop + 8paint + 1 inspection
Y=12shop + 12paint + 1.5 inspection

shop < 90
paint < 72
inspection < 10

What the heck am I doing wrong? I'd prefer a hint in the right direction over the solution.

Thanks,

Matt

Answer 1

There are two variables: deluxe, and custome

There are three constraints.

Plot on a graph the number of deluxe,custom you can make at the same time.

Start with the axis, and fill in the chart, it is only six points. Your max profit will be at one of the corners.