1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X1 + X2 + X3 + X4
Subject to: X1 + X4 = 12 (shift 1)
X1 + X2 = 15 (shift 2)
X2 + X3 = 16 (shift 3)
X3 + X4 = 14 (shift 4)
all variables = 0

Find the optimal solution using QM.
How many workers would be assigned to shift 1?

a. 12
b. 13
c. 0
d. none of the above


2. When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and:
finding the profit at every corner point of the feasible region to see which one gives the highest value.
a. moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
b. locating the point that is highest on the graph.
c. none of the above.
d. all of the above.

3. Multiple optimal solutions can occur when the objective function is __________ a constraint line.
a. unequal to
b. equal to
c. linear to
d. parallel to

4. When applying linear programming to diet problems, the objective function is usually designed to:
a. maximize profits from blends of nutrients.
b. maximize ingredient blends.
c. minimize production losses.
d. maximize the number of products to be produced.
e. minimize the costs of nutrient blends.

5. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:
a. same product mix, different total profit.
b. different product mix, same total profit as before.
c. same product mix, same total profit.
d. different product mix, different total profit.

6. The corner point solution method:
a. will yield different results from the isoprofit line solution method.
b. requires that the profit from all corners of the feasible region be compared.
c. will provide one, and only one, optimum.

d. requires that all corners created by all constraints be compared.

e. will not provide a solution at an intersection or corner where a non-negativity constraint is involved.

7. When using Excel's Solver to input and solve a linear programming problem, it is essential that one perform an additional task before submitting the formulation. That important additional function is:
a. guessing the values of the variables.
b. putting in a value for the objective function.
c. choosing the options for assuming both a linear model and non-negative variables.
d. resetting the parameters.
e. none of the above.

8. ____________ is used to analyze changes in model parameters.
a. Optimal solution
b. Feasible solution
c. Sensitivity analysis
d. None of the above