SOLUTION: Could you solve this problem for me I worked it out somewhat just want to know final answer and steps needed to get it. Up to this points I came up with: A= 3x+3y+2z less the

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Question 453169: Could you solve this problem for me I worked it out somewhat just want to know final answer and steps needed to get it.
Up to this points I came up with:
A= 3x+3y+2z less then or equal to 182
B= 7x+4y+z less then or equal to 122
profit equals 3192x+3648y
What are the steps after this problem to finish it and how would i grab it?
A manufacturer has the capacity of producing two different highly technological military devices(device A and B). There are three phases to the construction of these two devices, the first is the construction of the components for the devices, the second is the assembly of the units, and the the third is the finishinig and testing of the devices. for each unit of device A it takes 3 hours to create the components, 3 hours to assemble the device, and 2 hours for finishing for a profit of $3,192. For each unit of device B it takes7 hours to create the components, 4 hours to assemble the device, and 1 hour for finishing for a profit of $3648. Each day there are 182 hours available for the construction of the components, 122 hours available for the assembly of the devices, and 68 hours available for the finishing of the devices. Find the number of devices of A and B that they should create each day to maximize profit.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Your objective function is correct, but you are way out to lunch on your constraints.

Your objective function is using and to represent the number of device A and device B units produced, hence for the constraints, and have to mean the same thing.

It takes 3 hours to create each set of components for type A and 7 hours to create the set of components for type B, and you have a total of 182 hours available for component creation, so:

Likewise, the other two labor hours constraints are:

and

You should also constrain both and to be non-negative since you cannot manufacture a negative number of things (except maybe if you were using anti-matter -- but that is another problem altogether).

I presume you know how to graph a 2 variable inequality. The graphs of all of your constraints will create an irregular pentagon region of feasibility. You will need to solve for the intercepts and the points of intersection. A fundamental theorem of Operations Research says that a unique optimum solution exists, then it will be one of the vertices of the region of feasibility.

Find the ordered pairs that describe the vertices of your feasible pentagon and test each one in the objective function. The one that gives the biggest result is your solution.

John

My calculator said it, I believe it, that settles it