I've worked out the problem below. Can someone check this and let me know whether my answer sounds correct or not..Thanks!
The manager of a supermarket meat department finds that there are 160 pounds of round steak, 600 pounds of chuck steak, and 300 pounds of pork in stock on Saturday morning. From experience, the manager knows that half of these quantities can be sold as straight cuts. The remaind meat wil have to be ground into hamburger patties and picnic patties for which there is a large weekend demand. Each pound of hamburger pattie contains 20% ground round and 60% ground chuck. Each pound of picnic paties contains 30% ground pork and 50% ground chuck. The remainder of each product consists of an inexpensive nonmeat filler that the store has in unlimited quantities. How many pounds of each product should be made if the objective is to maximize the amount of meat used to make the patties?
My answer is below:
Round Steak Chuck Steak Pork
Pounds 160 600 300
Straight 80 300 150
Cuts__________________________________________
Left Over 80 300 150
to ground
Hamburger patties = 20r + 60c + 20f
Picnic patties = 50c + 30p +20f
Objective Function: Pounds = hx + py
Subject to the constraints:
x + py = 100
hx + y = 100
x > 0
y > 0
Answer: 83 1/3 hamburgers
500 picnic patties
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