Read the sections "Model Formulation" (p.32), and "Characteristics of Linear Programming Problems" (p. 57). State whether each equation below is linear, and if it is not, explain why not?

a. Y = mx + b True / False b. Y = ax^2 True / False c. Y = ax1 + bx2 + cx3 True / False d. Y = ax2 + bx + c True / False e. Y = (a/d)x + (b/a)x + c True / False

2. Solve the problem graphically using the below steps.

maximize z = 3x1 + 6x2

subject to

3x1 + 2x2 18

x1 + x2 5

x1 4

x1, x2 0

A. Create a table for the data given in the problem

B. Define the below as words = mathematical symbols

a. Decision variables:

b. Parameters:

C. Write out the mathematical formulation of the problem

D. Treating constraints as equalities, solve for the axis-constraint intersection points.

E. Create a graph of the solution space, including all your constraints.

F. Solve for the intersection(s) of constraints and plot on the above graph

G. List the extreme points and calculate their objective function values

H. Write out the problem solution in words as you relay it to the decision-maker.

Why is optimization a good management science technique to solve this problem as formulated?

3. Solve the problem graphically using the below steps.

The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats, and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03.

A. Create a table for the data given in the problem

B. Define the below as words = mathematical symbols

a. Decision variables:

b. Parameters

C. Write out the mathematical formulation of the problem

D. Treating constraints as equalities, solve for the axis-constraint intersection points

E. Create a graph of the solution space, including all your constraints.

F. Solve for the intersection(s) of constraints and plot on the above graph

G. List the extreme points and calculate their objective function values

H. Write out the problem solution in words as you relay it to the decision-maker.

Why is optimization a good management science technique to solve this problem as formulated?

4. Formulate a linear programming model for the below problem.

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: Sausage and Ham Labor (hr.): 0.010 and 0.024 Sausage (lb.) 0.10 and -- Ham (lb.) -- and 0.15 Flour (lb.) 0.04 and 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 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.

Enter and solve the problem in either excel, Excel QM, or QM for Windows. Paste into this document the table of results and the resultant graph