Question

Your surf shop sells two types of surf boards. the first, type a costs $272 and you make a $29 profit on each one. The second, type b, costs $136 and you make a $17 profit on each one. You can order no more than 50 surfboards this month, and you need to make at least $1210 profit on them. If you must order at least one of each type of surf board, how many of each type of surfboard should you order if you want to MINIMIZE your cost?

Answer 1

Not 100% sure about this but I think you just solve the simultaneous equations
29a+17b=1210
a+b=50
which gives a=30, b=20.

Answer 2

The actual optimization problem would look like the following, assuming x to be the quantity of type A and y to be the quantity of type B:

$$\min \qquad 272x + 136y \\
\text{s.t.} \qquad 29x+17y \geq 1210 \\
\qquad \qquad x \geq 1, y \geq 1
$$

This is a simple linear program, solve using any technique, the optimal solution is: x = 1, y = 1181/17. The min cost is 9720.

Answer 3

y turns out to be 69.47, hence, try out both 69 and 70 to see which one minimizes.

Answer 4

You can only order 50

Answer 5

Also, if you use a=30, b=20, you get a cost of $8500

Answer 6

well, then add

$$x+y \leq 50$$

in the constraints.

Answer 7

I think you'll get the same answer

Answer 8

right, it is just because the constraints becomes tight for those inequalities. The general procedure to solve the problem is the LP, which I mentioned above.

Answer 9

Refer to the attached Mathematica solution.