Project #52000 - Linear programming homework due 12/20/14 (5 problems)

 

A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are shown in the following table.

 

Product

Material 1 (lbs.)

Material 2 (lbs.)

Labor (hours)

A

3

2

4

B

1

4

2

C

5

none

3.5

 

Material 1 costs $7 a pound, material 2 costs $5 a pound, and labor costs $15 per hour. Product A sells for $101 a unit, product B sells for $67 a unit, and product C sells for $97.50 a unit. Each week there are 300 pounds of material 1; 400 pounds of material 2; and 200 hours of labor. Also, there is a weekly demand of at least 10 units of product C each week.

 

Solve the given problem scenario by formulating and setting up the problem in Excel Solver.

 

Directions:

Provide the written formulation in a word document. (Provide a complete description of the decision variables used along with their units and also label the constraints mentioned in the problem as completely as possible.)

 

The Excel set-up should provide clearly labeled values used for the decision variables, constraints, and objective function.

 

 

2.

A sports manufacturer produces two products: footballs and baseballs. These products can be produced either during the morning shift or the evening shift. The cost of manufacturing the football and the baseball in the morning shift is $20 each, and the cost of manufacturing the football and the baseball in the evening shift is $25 each. The amounts of labor, leather, inner plastic lining, and demand requirements are given as follows:

 

            Resource                                             Football           Baseball          

            Labor (hours/unit)                           0.75                      2     

            Leather (pounds/unit)                                7                         15     

            Inner plastic lining (pounds/unit)           0.5                        2     

            Total demand (units)                                 1500                1200    

 

Based on the information about the company, we know that the maximum labor hours available in the morning shift and evening shift are 5,000 hours and 2,000 hours, respectively, per month. The maximum amount of leather available for the morning shift is 15,000 pounds per month and 14,000 pounds per month for the evening shift. The maximum amount of inner plastic lining available for the morning shift is 2,000 pounds per month and 1,500 pounds per month for the evening shift. 

 

Solve the given problem scenario so as to minimize the production cost and determine the number of footballs and baseballs made by this company by formulating and setting up the problem in Excel Solver.

 

Directions:

Provide the written formulation in a word document. (Provide a complete description of the decision variables used along with their units and also label the constraints mentioned in the problem as completely as possible.)

 

 

The Excel set-up should provide clearly labeled values used for the decision variables, constraints, and objective function.

 

 

3.

In a small suburban town, firefighters work 8-hour shifts. Assume there are 6 shifts each day that are divided into six 4-hour periods. The minimum number of firefighters needed on each shift is illustrated below.

 

            Shift                            Number of Firefighters Needed

            Midnight–4 a.m.                   5

            4 a.m.–8 a.m.                         6

            8 a.m.–Noon                          10

            Noon–4 p.m.                          12

            4 p.m.–8 p.m.                         8

            8 p.m.–Midnight                   5

            

Firefighters must report to work at the beginning of the above time periods and must work eight consecutive hours.

 

Solve the given problem scenario to determine the minimum number of firefighters needed on each shift by formulating and setting up the problem in Excel Solver.

 

Directions:

Provide the written formulation in a word document. (Provide a complete description of the decision variables used along with their units and also label the constraints mentioned in the problem as completely as possible.)

 

 

The Excel set-up should provide clearly labeled values used for the decision variables, constraints, and objective function.

 

5.

A manufacturer of rotary pumps is planning production for the next four months. The forecast demand for the rotary pumps is shown in the following table. 

 

Rotary pump             SEP            OCT           NOV          DEC

Standard                    650            875            790            1,100

Heavy duty                 900            350            1,200         1,300

 

At the beginning of September, the warehouse is expected to be completely empty. There is room for no more than 1,800 rotary pumps to be stored. Holding costs for both types are $5 per unit per month. Because workers are given time off during the holidays, the manufacturer wants to have at least 800 standard rotary pumps and 850 heavy duty rotary pumps already in the warehouse at the beginning of January.

 

Production costs are $125 per unit for standard rotary pumps and $135 per unit for heavy duty rotary pumps. Because demand for raw materials is rising, production costs are expected to rise by 5% per month through the end of the year.

 

Labor to make the standard rotary pump is 0.45 hours per unit; making heavy duty rotary pumps takes 0.52 hours per unit of labor. Management has agreed to schedule at least 1,000 hours per month of labor. As many as 200 extra hours per month are available to management at the same cost, except during the month of December, when only 100 extra hours are possible. 

 

Solve the given problem scenario to determine the production schedule for standard and heavy duty rotary pumps for the four months by formulating and setting up the problem in Excel Solver.

 

Directions:

Provide the written formulation in a word document. (Provide a complete description of the decision variables used along with their units and also label the constraints mentioned in the problem as completely as possible.)

 

 

The Excel set-up should provide clearly labeled values used for the decision variables, constraints, and objective function.

Subject Mathematics
Due By (Pacific Time) 12/20/2014 12:00 am
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