Question 1

The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium while minimizing cost.
(1). Formulate a cost minimization linear programming model for this problem.
(2). Solve this model by using graphical method (the objective function approach).
(3). Solve the model by using the Enumeration approach.
(4) Analyze slack/surplus for each constraint.

Question 2

The Pinewood Furniture Company produces chairs and tables from two resources Ac€?o labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. 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 tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem.

A. Formulate a linear programming model for this problem.

B. Solve the model by using graphical analysis.

2. In Problem 2, how much labor and wood will be unused if the optimal numbers of chairs and tables are produced?

Question 3

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 one gram of ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of antibiotic 2 are required and the ingredients contribute 1 unit each per gram. 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 drug in order to meet the antibiotic requirements at the minimum cost.

A. Formulate a linear programming model for this problem.

B. Solve the model by using graphical analysis.

Question 4

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 (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. a. Formulate a linear programming model for this problem b. Solve this model by using computer c. Identify and explain the shadow prices for each of the resource constraints. d. Which of the resources constraints profit the most? e. Identify the sensitivity ranges for the profit of a sausage biscuit and the amount of sausage available. Explain these sensitivity ranges.

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Status NEW Posted 12 Feb 2019 07:02 AM My Price 10.00

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file 1550038641-The Kalo Fertilizer Company.xlsx preview (292 words )

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file 1550038663-The Pinewood Furniture Company.docx preview (56 words )

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file 1550038677-The Elixer Drug Company.docx preview (87 words )

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file 1550038695-Burger Doodle Franchise.xlsx preview (17 words )

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