Question

LP Graphical Method Problems

1) MAXIMIZATION PROBLEM - 4 PTS

Objective Function: Maximize Profit: 5X + 3Y

Subject to the constraints:

5 X + 2 Y ≤ 40

3 X + 6 Y ≤ 48

X ≤ 7

2 X − Y ≥ 3

X , Y ≥ 0

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2) MINIMIZATION PROBLEM - 4 PTS

Objective function: Minimize Cost: 3X + 7Y

Subject to the constraints:

9 X + 3 Y ≥ 36

4 X + 5 Y ≥ 40

X − Y ≤ 0

2 X ≤ 13

X , Y ≥ 0

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3) MARRIOTT TUB - 6 PTS

For this problem, make sure to include the complete LP Formulation in your answers.

Example:

Objective Function: Maximize what? or Minimize what?

Subject to the following constraints: (then list down your complete constraints)

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The Marriott Tub Company manufactures two lines of bathtubs, Models A and B.

Every tub requires blending a certain amount of steel and zinc. For the next production run, the company has available a total of 24,500 pounds of steel and 6,000 pounds of zinc.

Each model A bathtub requires a mixture of 120 pounds of steel and 20 pounds of zinc and yields a profit of $90. Each Model B bathtub produced earns a profit of $70 and it requires 100 pounds of steel and 30 pounds of zinc. To maintain an adequate supply of both models, the company would like the number of model A tubs made to be no more than 5 times the number of model B tubs.

Find the best product mix of bathtubs.

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4) ANA'S CAFE - 6 PTS

For this problem, make sure to include the complete LP Formulation in your answers.

Example:

Objective Function: Maximize what? or Minimize what?

Subject to the following constraints: (then list down your complete constraints)

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Ana’s Café does a large lunchtime carry out business. The café offers two burrito specials: Mild and Spicy. The profit on one serving of Mild is $0.58, while the profit on one serving of Spicy is $0.45.

Each serving of Mild requires 0.15 pounds of beef, 0.36 cups of beans, and 3 ounces of salsa. Each serving of Spicy requires 0.30 pounds of beef, 0.40 cups of beans, 2 ounces of salsa and 5 ounces of special hot sauce.

Today, Ana checked her pantry and found out that she only has 8.5 pounds of beef, 13 cups of beans, 95 ounces of salsa, and 125 ounces of hot sauce available. Demand for both types of burritos is unlimited.

What should Ana do for lunch?

Answer 1