Another Interesting Solution Using Solver in Microsoft Excel
Need help with this Linear Programming Problem (Solver)?
To make one package of all beef hot dogs, a manufacturer uses 1 lb of beef; to make one package of regular hot dogs, the manufacturer uses 1/2 lb each of beef and pork. The profit on the all-beef hot dogs is 40 cents per pack and the profit on regular hot dogs is 30 cents per pack. If there are 200 lbs of beef and 150 lbs of pork available, how many packs of all-beef and regular hot dogs should the manufacturer make to maximize profit? What is the profit?
You can solve the problem in many ways. We can use simple Algebra or Solver and the advantages of the latter become obvious with the increase in the complexity of the problem.
Entering the data in the Microsoft Excel worksheet properly is half the battle won. The easiest way is to enter the data as the user narrates it. So we have entered the data for manufacturing one hot dog of each kind in cells B4:C5 and calculated the profit in range E4. The ingredients required, the quantity used in each hot dog, the total quantity used and the total quantity of meat available is entered into range B8 to E9 with appropriate headers.The quantity of meat used to manufacture the hot dogs is calculated based on the quantity of hot dogs produced. We also apply logical constraints like the calculations cannot have negative values in the production of hot dogs and the quantity of raw material used for production can never exceed what is available in the ware-house. Although these things are quite logical to the human brain the computer and its program need to be told this clearly!
Watch the video below to see how Microsoft Excel’s Solver performs its magic once you tell it what to do: