Linear bull****?

Question

Solve this linear programming mixture problem: A small stereo manufacturer makes a receiver and a CD player. Each receiver takes 8 hours to assemble, 1 hour to test and ship, and earns a profit of $30. Each CD player takes 15 hours to assemble, 2 hours to test and ship, and earns a profit of $50. There are 160 hours available in the assembly department and 26 hours available in the testing and shipping department. What should the production schedule be to maximize profit? What is the maximum profit?

I've got:

x being the stereos
y being the CD players

theres 160 hours for assembly so
8x+15y<160

theres 26 hours for shipping
x+2y<26

Then
x>0 and y>0 as givens
How do I graph the feasible region?
I don't have a graphing calculator =[

Answer 1

You shouldn't need a graphing calculator to do this.

For each straight line that defines an inequality, set one variable equal to 0 and solve for the other. this gives the x and y intercepts. Once you have two points, you can draw the line.

And it is not bull. Linear programming is used in the real world to do some real decision making.

Answer 2

You should solve for y in both inequalities first.

8x + 15y < 160
15y < 160 - 8x
y < (160 - 8x)/15
y < 32/3 - (8/15)x

x + 2y < 26
2y < 26 - x
y < 13 - x/2

Then it should be easier to plug in values of x.

By the way, I think those '<' signs should be '<=' signs. (less than or equal to)