How do you determine the objective function in a linear programming (systems of equations)?

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How do you determine the objective function in a linear programming (systems of equations)?

Mathematics
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sorry i cant explain it..do you have an example?
Yes....the ones problems in the past have always had that given. A shoe manufacturer makes outdoor and indoor soccer shoes. Ther is a two-step manufacturing process for both kinds of shoes. Each pair of outdoor shoes requires 2 hours of processing in step one and 1 hour in step two. Indoor shoes require 1 hour of processing in step one and 3 hours in step two. The company has only 40 hurs of labor available for step one and 60 hours available for step two. a.) identify the variables b.) write the objective function c.) write the constraints d.) graph the feasible region e.) identify the maximum profit and how many of each type of shoe should be produced to reach this profit
I have the equations 2x + y = 40 and x + 3y = 60 to graph....correct?

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yes except use inequalities 2x+y<=40 so x represents num of outdoor shoes y represents num of indoor shoes
so those would be your constraints
ok what about x>=0 and y>= 0 also?
to find objective function here look at what they want to know, what do they want to maximize? profit so we have define profit in terms of our variables
yes x>=0, y>=0
ok, so how do you come up with the equation for that?
well profit = sales revenue - cost of labor revenue = price * quantity is there additional info
nope, I typed the entire problem. Isn't that part missing??
ok since we are not given any prices we can assume labor costs nothing and all shoes sell at equal value so we want to make as many shoes as possible within constraints profit = x + y, which is just the total num of shoes made
oh, that's easy then! Just plug in your contraints and solve to see which produces the largest value (profit)
yep once you graph your constraints pick end points along outside of bounded region plug them into profit function good luck
got that!! Thanks!!!!!
no problem

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