LP Word Problem Construction

Question

I am having difficulty constructing the constraints on a word problem as follows:

The Brite-lite Company receives an order for 78 floor lamps, 198 dresser lamps, and 214 table lamps from condoski Corp. Brite-Lit ships orders in two types of containers. The first costs \$15 and can hold 2 floor lamps and 4 table lamps or 2 floor lamps and 2 table lamps and 4 dresser lamps. The second costs $25 and can hold 3 floor lamps and 8 table lamps or 8 table lamps and 12 dresser lamps. Minimize the cost of the containers to hold the order.

The fact that the containers can hold 2 different quantities each is the difficulty I am having. Would it be correct to just give 4 different variables, 2 for each container? Giving:

Minimize

$15(x_1 + x_2) + 25(y_1 + y_2) = z$

Subject to

$2x_1 + 2x_2 + 3y_1 \ge 78$

$4x_2 + 12y_2 \ge 198$

$4x_1 + 2x_2 + 8y_1 + 8y_2 \ge 214$

$x_1, x_2, y_1, y_2 \ge 0$

$\LaTeX$ hint: you can use \ge to get $\ge$, which looks nicer than $\gt =$ — Ross Millikan, Feb 23 '15 at 17:21

score 2 · Answer 1 · answered Feb 23 '15 at 17:20

2

Yes, you have the right approach. Your three subject to equations should be inequalities using $\ge$, however. You need enough room for all the products, but it seems it should be acceptable to leave empty space if you can reduce the cost.

answered Feb 23 '15 at 17:20

Ross Millikan

374,822

Ah yes that would make more sense, thank you :) – Vivid Feb 23 '15 at 17:31

LP Word Problem Construction

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