Advanced Math/Pre calc

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Expert: - 1/26/2011


Question
A manufacturer of metal widgets make two types, A and B. Each type A widget requires 0.5 hours of cutting, 1.5 hours of welding and 1.0 hours of finishing. Each type B widgets requires 0.5 hours of cutting, 1.0 hours of welding and 1.5 hours of finishing. Each day 15 hours of cutting time, 36 hours of welding time and 42 hours of finishing time are available. If the profits on a type A widget and type B widget are $3 and $4, respectively, how many of each type widget should be made each day to maximize total profits?

Answer
A) 0.5, 1.5, 1.0
B) 0.5, 1.0, 1.5
Total) 15, 36, 42
Profit for A, B is $3, $4

Since A and B both take 0.5 hours of cutting, ignore that and at the end see if 0.5A + 0.5B <= 15

Take 1.5A + 1.0B = 36 and 1.0A + 1.5B = 42.

I believe this comes out to A = 9.6, B = 21.6.
Now since we are making widgets, round down to the nearest integer, giving A = 9 and B = 21.
Since 0.5(9) + 0.5(21) = 15, that uses up all of the cutting hours.
Since 1.5*9 + 21 = 34.5, there are 1.5 hours of welding unused.
Since 1*9 + 1.5*21 = 40.5, there are also 1.5 hours of finishing unused.

The last thing to do is to try increasing B by 1, which decreases A by 1.
This still satisfies equation 1, but test to see if it satisfies equations 2 and 3.
If it does, the profit will go up since B gives $4 and A only gives $3.

If it works, do again.

Now this could have been done as an operations research question,
but that's not the class you're in.

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