# Linear Programming Model

Please see attached file for full problem description.

1. In problem 28 in Chapter 1, when McCoy wakes up Saturday morning, she remembers that she promised the PTA she would make some cakes and/ or homemade bread for its bake sale that afternoon. However, she does not have time to go to the store to get ingredients, and she has only a short time to bake things in her oven. Because cakes and breads require different baking temperatures, she cannot bake them simultaneously, and she has only 3 hours available to bake. A cake requires 45 minutes to bake, and loaf of bread requires 30 minutes. The PTA will sell a cake for $10 and loaf of bread for $6. Marie wants to decide how many cakes and loaves of bread she should make.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.

5. The Kalo Fertilizer Company makes a fertilizer using two chemical that provide nitrogen and 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 20 ounces of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium while minimizing cost.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.

18. Solve the following linear programming model graphically:

Maximize Z= 1.5x1 + x 2

Subject to

x1 ≤ 4

x2 ≤ 6

x1+ x2 ≤ 5

x1, x2 ≤ 0

38. A manufacturing firm produces two products. Each product must undergo an assembly process and finishing process. It is then transferred to the warehouse , which has space for only a limited number of items. The firm has 80 hours available for assembly and 112 hours for finishing, and it can store a maximum of 10 units in the warehouse. Each unit of product 1 has a profit or $30 and requires 4 hours to assemble and 14 hours to finish. Each unit of product 2 has a profit of $70 and requires 10 hour to assemble and 8 hours to finish. The firm wants to determine the quantity of each product to produce in order to maximize profit.

A. Formulate a linear programming model for this problem.

B. Solve this model by using graphical analysis.

#### Solution Summary

This posting provides several problems on linear programming analysis along with graphical analysis. Some of the case examples include: McCoy, Kalo Fertilizer Company and a Manufacturing firm.