Indicate whether the statement is true or false. 
1. An extreme point of the feasible region can include negative values of coordinates.

2. In stationary time series there is no significant upward or downward trend in the data over time.

3. Mathematical programming is an approach that involves determining how to allocate the resources in such a way as to maximize profits or minimize costs.

4. Examining the effect of changes in the RHS values of constraints is part of the answer report.

5. The TREND( ) function can be used to calculate the estimated values for linear regression models.

6. Shadow prices represent the marginal values of the resources in an LP problem,

7. Seasonality is a regular, repeating pattern in the data that takes longer than 1 year to complete.

8. Objective cell, variable cells and constraint cells are terms used in Excel solver to describe the purpose of the cells.

9. Solver can be used to estimate model parameters when the time series is stationary and additive seasonal effects are present.

10. The weighted moving average technique is a special case of the moving average technique.

11. If a shadow price is positive for a maximization problem, a unit increase in the RHS value of the associated constraint results in a decrease in the optimal objective function value.

12. Good decisions always result in good outcomes.

13. Humans usually do not make errors in estimation due to anchoring and framing effects.

14. Excel and other spreadsheets contain an addon called solver.

Indicate the answer choice that best completes the statement or answers the question. 
Exhibit 3.1
The following questions are based on this problem and accompanying Excel windows. Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
The LP model for the problem is

15. Refer to Exhibit 3.1. What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of carpentry used?

16. Why would someone wish to use a spreadsheet model?

17. In a model Y=f(x_{1}, x_{2}), Y is called:

18. In a mathematical formulation of an optimization problem, the objective function is written as z=2x_{1}+3x_{2}. Then:

20. What needs to be done to the two constraints in order to convert the problem to a standard form?

Exhibit 3.3
The following questions are based on this problem and accompanying Excel windows. Jack’s distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer’s requirements and maximize profit.

21. Refer to Exhibit 3.3. What formula should be entered in cell D11 in the accompanying Excel spreadsheet to compute the total liters of alcohol supplied?

22. Binding constraints have

24. A linear formulation means that:

26. Which step of the problemsolving process is considered the most important?

28. The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits.
X_{1} = number of product 1 produced in each batch
How much profit is earned per each unit of product 2 produced?

29. The symbols X_{1}, Z_{1}, Dog are all examples of

30. Which of the following categories of modeling techniques involves determining the value of a dependent variable based on specific values of independent variables?

31. When performing sensitivity analysis, which of the following assumptions must apply?

32. The first step in formulating a linear programming problem is

33. Mathematical programming is referred to as

Exhibit 3.2
The following questions are based on this problem and accompanying Excel windows. The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.

34. Refer to Exhibit 3.2. Which of the following statements will represent the constraint for just assembly hours?

36. A solvable problem must have:

37. The coefficients in an LP model (c_{j}, a_{ij}, b_{j}) represent

38. If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value?

42. A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in longterm bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
Formulate the LP for this problem. 
44. A hospital needs to determine how many nurses to hire to cover a 24 hour period. The nurses must work 8 consecutive hours but can start work at the start of 6 different shifts. They are paid different wages depending on when they start their shifts. The number of nurses required per 4hour time period and their wages are shown in the following table.
What values would you enter in the Analytic Solver Platform (ASP) task pane for the following cells for this Excel spreadsheet implementation of the formulation for this problem? Objective Cell: Variables Cells: Constraints Cells:

46. Robert Hope received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a midterm exam, and a final exam. Robert’s grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Robert’s task somewhat by adding the following stipulations:
Formulate an LP model for Robert to maximize his numerical grade. 
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