# Analysis of Linear Programming

Problems must be completed in QM or Lingo 10.

1.0 Given the following linear programming problem:
Min Z = 2x + 8y
Subject to (1) 8x + 4y 64
(2) 2x + 4y 32
(3) y 2

What is the minimal solution?
Use Lingo10 or QM to solve. Include your solution screen shots

2.0 Max Z = \$0.30x + \$0.90y
Subject to : 2x + 3.2y 160
4x + 2y 240
y 40
x, y

Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2?
Use Lingo10 or QM to solve. Include your solution screen shots

3.0 The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are \$2 per bottle, and profits for dark beer are \$1 per bottle.

What is the objective function?
What is the constraint for malt?
What is the constraint for wheat?
Use Lingo10 or QM to solve. Include your solution screen shots

4.0 The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one “8 hour” shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drink are \$2.00 per case. How many cases of regular and how many cases of diet soft drink should Whoppy produce to maximize daily profit?

What is the objective function?
What is the constraint for Time?
What is the constraint for Syrup?
Use Lingo10 or QM to solve. Include your solution screen shots

5.0 Consider the following transportation problem:
1 2 Supply
1 5 6 100
2 4 2 200
3 3 6 150
4 9 7 50
Demand 250 250

What is the objective function?
What are the Supply side constraints?
What are the Demand side constraints?
Use Lingo10 or QM to solve. Include your solution screen shots

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