Mat 540

MAT 540 Homework #4 | | |

This homework covers six problems from chapter 2: 6, 42, 46, 48, 56, and 58. For those problems requiring you to show the programming model, you need to state the model just like the pottery company example at the bottom of page 34. This includes labeling the cosntraints. For those problems requiring you to provide the graphical solution, you are to provide the extreme points of the feasible region in the form of (x1 = , x2 = , Z = ) and identify which is the optimum solution. You need not list the origin as an extreme point, because it is a given. DO NOT SHOW THE GRAPH. Displaying the extreme points shows me that you have done the graph. The short answer fields are text only fields. You can always enter your answers below and then copy and paste your answers into the short answer text fields on the eCollege exam when you are ready. This will minimize the amount of time spent online doing the exam, and provide you sufficient time to check your answers prior to hitting the submit button on the exam.

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1. Problem 2-6 a (6.0 points)

Formula a linear programming model for this problem.

Answer:

| |Chairs(x) |Tables(y) |Available |

|Labor |8 |10 |80 |

|Wood |2 |6 |36 |

|Profit |$400 |$100 | |

Maximize[pic]Profit P = 400x + 100y

Subject to

8x + 10y ≤ 80 hours of labor

2x + 6y ≤ 36 pounds of wood

0 ≤ x ≤ 6 and y ≥ 0

Where,

x = number of chairs produced,

y = number of tables produced

2. Problem 2-6 b (6.0 points)

Solve this problem using graphical analysis.

Answer: The company should produce 6 chairs and 3 tables each day in order to maximize profit.

The polygon OABCD represnts the solution area of the problem stated. The value of x and y at points A, B, C and D are: A (0, 6),...