Exam 3: Modeling and Solving Lp Problems in a Spreadsheet

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Which type of spreadsheet cell represents the left hand sides (LHS) formulas in an LP model?

How many decision variables are there in a transportation problem which has 5 supply points and 4 demand points?

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

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 -Refer to Exhibit 3.1. Which cells should be changing cells in this problem?

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What formulas should be entered into cells E5 and D8:D10 to implement this model?

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. The following table summarizes the data for the problem. What are the key formulas for this Excel spreadsheet implementation of the following formulation?

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 mid-term 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: The following LP model allows Robert to maximize his numerical grade. What values would you enter in the Risk Solver Platform (RSP) task pane for the cells in this Excel spreadsheet implementation of this problem? Objective Cell: Variables Cells: Constraints Cells:

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production. Enter the numbers in the appropriate cells of range B5:F10 in the Excel spreadsheet to solve this problem based on the following formulation.

What action is required to make Risk Solver Platform (RSP) solve a specified problem?

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 4-hour time period and their wages are shown in the following table. Enter the numbers in the appropriate cells of ranges B6:G11 and B13:G13 in the Excel spreadsheet to solve this problem based on the following formulation.

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. -Refer to Exhibit 3.3. Which of the following statements could represent a constraint in this problem?

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 long-term 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.

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 -Refer to Exhibit 3.1. Which of the following statements represent the carpentry, varnishing and limited demand for desks constraints?

Which tab in the Risk Solver Platform (RSP) task pane is used to define an optimization problem?

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available. The following table summarizes the data for the problem. Enter the numbers in the appropriate cells of ranges B12:D12 and E8:F12 in the Excel spreadsheet to solve this problem based on the following formulation.

Spreadsheet modeling is an acquired skill because

How many constraints are there in a transportation problem which has 5 supply points and 4 demand points? (ignore the non-negativity constraints)

The following questions are based on this problem and accompanying Excel windows. A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter. -Refer to Exhibit 3.5. Which cells are changing cells in the accompanying Excel spreadsheet?

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. -Refer to Exhibit 3.2. What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total profit?