# Formulate L.P. Model and Solve using Graphical Analyis

See attached file.

Four Linear Programming problems:

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 hrs of processing time on line 1, while on line 2 product 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.

a) Solve this model using graphical analysis

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 cost $3 per pound, and ingredient 2 cost $5 per pound. The company asked 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.

The Elixir 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 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 each contribute 1 unit per gram. At least 12 units of antibiotic 3 are required; a gram of ingredient1contributes 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 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.

a) Solve this model using graphical analysis

A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square yards of wool and 4 hours of labor. The profit for a coat is $50, and the profit for slacks is $40. The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.

a. Formulate a linear programming model

b. solve model by graphical analysis

https://brainmass.com/statistics/linear-regression/formulate-l-p-model-solve-using-graphical-analyis-316735

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached files.