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Question 1110667: A dealer has 7600 pounds of peanuts, 5800 pounds of almonds, and 3000 pounds of cashews to be used to make two mixtures. The first mixture wholesales for $8.44 per pound and consists of 60% peanuts, 30% almonds, and 10% cashews. The second mixture wholesales for $3.17 per pound and consists of 20% peanuts, 50% almonds, and 30% cashews. How many pounds of each mixture should be made to maximize revenue? Find the maximum revenue.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52814)   (Show Source):
You can put this solution on YOUR website! .
Let X and Y be the amounts (in pounds) of each mixture.
The Revenue function is Z = 8.44*X + 3.17*Y.
The constraints are these inequalities:
0.6X + 0.2Y <= 7600 (1) (peanuts)
0.3X + 0.5Y <= 5800 (2) (almonds)
0.1X + 0.3Y <= 3000 (3) (cashews)
You need to find the maximum of the objective function under these restrictions (1), (2), (3) and X >= 0, Y>= 0.
At this point, the formulation/(the setup) of the linear optimization problem is COMPLETED.
Further, you can apply the Linear programming method and solve the problem using a standard Geometry visualization approach.
On how to do it, you can learn from the lesson
- Solving minimax problems by the Linear Programming method
in this site.
Answer by greenestamps(13203)  (Show Source):
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