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Question 451696: I need help learning how to start and finish these three problems. My linear programming is kind of sketchy so if you can explain it better than my teacher it would be greatly appreciated.
First problem asks for me to" Minimize the objective function 1/2x+3/4y subject to the constraints
2x+2y greater than equal to 8
3x+5y greater than equal to 16
X greater than equal equal to 0
y greater than equal to 0
Second problem goes as follows" n electronics company has factories in Cleveland and Toledo that manufacture three head and four head VCR's. Each day the Cleveland factory produces 500 three head VCRs and 300 four head VCRs at a cost of $18000. Each day the Toledo factory produces 300 of each type of VCR at a cost of $15000. An order is received for 25,000 three head VCRs and 21,000 four head VCRs. For how many days should each factory operate to fill the order at the least cost.
"our teacher gave us the following answers Cleveland should operate for 20 days and Toledo should operate for 50 days. I just need to learn how to come up with those answers.
My last questions goes as follows " A contractor builds two types of homes. The first type requires one lot, $12,000 capital, and 150 labor-days to build and is sold for a profit of $2400. The second type of home requires one lot, $32,000 capital, and 200 labor days to build and is sold for profit of $3400. The contractor owns 150 lots and has available for the job $2,880,000 capital and 24,000 labor days. How many homes of each type should she build to realize the greatest profit? "Again he gave us a answer of 80 for type 1 and 60 for type 2. Any help would be appreciated thanks in advance.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
For the first problem use the theorem that says any optimum must be at the vertex of the feasible area polygon.
Graph your constraints and you will find that your feasible area is bounded by the x and y axes, the line segment joining the y-intercept of the 2x + 2y = 8 constraint boundary and the point of intersection of that constraint boundary and the 3x + 5y = 16 constraint boundary, and finally the line segment from the boundary intersection to the x-intercept of 3x + 5y = 16.
Hence, your three possible optimums are at (0, 4), (2, 2), and (5.33, 0)]
You can do your own coordinate geometry calculations to check my work on that part.
Now all you have to do is substitute the coordinate values from your three possible optimums into the objective function to see which one gives you he minimum result.
One problem per post there, Sparky. Read the instructions.
John
My calculator said it, I believe it, that settles it
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