Linear Programming Help! Need help setting up inequalities.?
I need some help with this annoying problem that I cant figure out how to set up
Here it is:
A company makes two models of light fixtures, A and B, each of which must be assembled and packed. The time required to assemble model A is 12 min and model B takes 18 min. It takes 2 min to package model A and 1 min to package model B. Each Week there are 240 hr available for assembly time and 20 hr for packing. If model A sells for 1.50 and model B sells for 1.70 and it costs .75 to produces model A and .85 to produce model B, how many of each should be made to max weekly profit.
I’ve been staring at this problem for like 3 hours trying to figure out what to do.. lol all I came up with was that you make .75 for each Model A you make and .85 Model B you make. Also the max of Model A you can make is 600 a week and the max of model B you can make is 800 a week.
I don’t know if that’s needed to solve the problem but Im stuck so some help would be greatly appreciated 
Let me run through the steps, even though you have some of it already. To formulate a linear program, first identify your decision variables. Usually the problem says in one of the sentences (often a question) what they are. Here, let’s just go ahead and call them A and B, the number of each light fixture to make.
Next construct the objective function. It says at the end to maximize the weekly profit, and you have to do a little bit of arithmetic first since they give you the selling price and the cost separately. Model A gives a profit of 1.50-.75=.75, and B gives profit of 1.70-.85=.85. So the objective function is .75A + .85B.
Since it’s profit, why not just make a million of both products? There are limited resources, like in most problems. Here the resources are the available labor for assembly, and the available labor for packing. Considering just the assembly step, product A consumes 12 minutes for each one you make, while product B consumes 18 of those minutes. And you have 240 hours available for assembly, so that’s 14400 minutes. So the constraint on the assembly hours is 12A + 18B <= 14400.
Similarly for packing, you have the constraint 2A + 1B <= 20*60=1200.
With the objective function plus these two constraints, hopefully you can graph them (if that's how your class is solving their LPs) and find the maximum profit.
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