Module 6 assignment

Module 6

A company produces two products that are processed on two assembly lines.Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 products 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit.
a. Formulate a linear programming model for this problem.
Please see the attachment.

The Pinewood Furniture Company produces chairs and tables from two resources-labor and wood. The company has 80 hours of labor and 36 pounds of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 pounds of wood, whereas a table requires 10 hours of labor and 6 pounds of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and table to produce each day in order to maximize profit.
a. Formulate a linear programming model for this problem.

The Elixer Drug Company produces a drug from two ingredients. Each ingredient contains the same three antibiotics, in different proportions. One gram of ingredient 1 contributes 3 units, and 1 gram of ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is $50. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the in order to meet the antibiotic requirements at the minimum cost.
a. Formulate a linear programming model for this problem.

22.

The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. Each type of biscuit requires the following resources.

Biscuit Labor(hr) Sausage(lb) Ham(lb) Flour(lb)

Sausage 0.010 0.10 ------- 0.04

Ham 0.024 ------ 0.15 0.04

The franchise has 6 hours of labor available each morning. The manager has a contract with a local grocer for 30 pounds of sausage and 30 pounds of ham each morning. The manager also purchases 16 pounds of flour. The profit for a sausage biscuit is $0.60; the profit for a ham biscuit is $0.50. The manager wants to know the number of each type of biscuit to prepare each morning in order to maximize profit.

Formulate a linear programming model for this problem.

On a separate spreadsheet, Solve the linear programming model formulated above graphically.

a) How much extra sausage and ham are left over at the optimal solution point? Is there any idle labor time?

b) What would the solution be if the profit for a ham biscuit were increased from $0.50 to $0.60?

c) What would be the effect on the optimal solution if the manager could obtain 2 more pounds of flour?

24. The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. The two types of biscuits require the following resources:

Biscuit Labor Sausage Ham Flour
Sausage (X1) 0.010 0.10 0.00 0.04
Ham (X2) 0.024 0.00 0.15 0.04

1. I dentify and explain ther shadow prices for each resource constraints.
2. Which resource constaints profit the most
3. Identify the sensitivity ranges for the profit of a sausauge biscuit and the amount of saisage available. Explain these sensitivity ranges