1. Acme Inc must send a representative to each of eight different satellite locations. Eight Acme representatives have been identified for the assignments. One representative will be sent to each of the eight satellite locations. In order to make the assignments each representative has been asked to rank their preferences from 1 – most favorable assignment to 8 – their least favorable assignment. The rankings appear in the table below. Determine which representative should be sent to each location in order to minimize the rankings and avoid sending representatives to the least favorable locations. Turn in computer printout along the answers

Locations

NYC CHI BOS N.O LA LV MIA MIN

Representatives

Professor Plum 3 4 6 1 7 8 5 2

Colonel Mustard 2 3 7 4 5 1 6 8

Ms Scarlett 2 8 6 5 1 3 4 7

Mrs. White 7 5 6 3 4 1 2 8

Miss Peacock 1 3 7 2 5 6 8 4

Mr. Green 7 6 5 3 8 1 2 4

The Butler 1 2 5 8 6 7 3 4

French Maid 5 3 4 1 2 8 6 7

2 Frugal Rent-A-Car has eight store lots in the Greater St. Louis Metropolitan area. At the beginning of each day, they would like to have a predetermined number of cars available at each lot. However, since customers renting a car may return the car to any of the eight lots, the number of cars available at the end of the day does not always equal the designated number of cars needed at the beginning of the day. Frugal would like to redistribute the cars in the lots to meet the minimum demand and minimize the time needed to move the cars.

Table I below, summarizes the results at the end of one particular day.

Table II below summarizes the time required to travel between the lots.

Solve the problem in order to determine how many cars should be transported from one lot to the next. Turn in computer printout along the answers

Table I Lot

Cars 1 2 3 4 5 6 7 8

Available 37 20 14 26 40 28 38 52

Desired 30 25 20 40 30 20 30 60

Table II To (in minutes)

From 1 2 3 4 5 6 7 8

1 -- 12 17 18 10 20 40 35

2 14 -- 10 19 16 15 28 32

3 14 10 -- 12 8 9 34 26

4 8 16 14 -- 12 15 44 38

5 11 21 16 18 -- 10 24 28

6 24 12 9 17 15 -- 36 35

7 38 30 32 40 25 38 -- 29

8 30 34 28 35 31 33 31 --

3. Minus Mufflers provides three types of automobile service for their customers – (1) extraneous muffler replacements, (2) bogus radiator repairs, and (3) unnecessary brake-pad replacements. Three of Minus’s employees do all the work. Mr. Henry is the only employee customers are allowed to talk to. Mr. Henry’s job includes, greeting the customers, explaining what is wrong with their car, the total costs involved and handling the paper work. A second employee, A. Capone is the inspector. A. Capone is responsible for examining the cars when they arrive at Minus and finding something wrong with the car. The third employee, Max, does all the repair work. The time required by each employee for each repair and the maximum number of hours each employee is willing to work per week is given in the table below. Minus ads guarantee their mufflers for the lifetime of the car. Therefore to avoid having to replace a muffler for free, Minus never installs their own brand, but rather installs A-1 mufflers. Minus has a contract to receive up to 40 A-1 mufflers per week (thus a maximum on only 40 muffler repairs can be performed each week). In addition, A Capone believes that at least 30% of the repairs should be radiator repairs. For kickback purposes, Mr. Haney requires that no more than 50% of repairs involve brake pad replacements. Finally, Max is unwilling to spend more than half of his actual working time (not the Maximum number of hours worked) performing radiator repairs. Formulate the LP model to maximize weekly profit and determine how many repairs of each time should be conducted per week.

Mr. Haney A.Capone Max

Service Profit time/repair time/repair time/repair

Muffler $70 15 minutes 10 minutes 30 minutes

Radiator $180 30 minutes 15 minutes 60 minutes

Brakes $95 15 minutes 15 minutes 20 minutes

Max hours/week 35 hours 25 hours 65 hours

4. G and P Manufacturing would like to minimize the labor cost of producing dishwasher motors for a major appliance manufacturer. Although two models of motors exist, the finished models are indistinguishable from one another; their cost difference is due to a different production sequence. The time in hours required for each model in each production area is tabled below along with the labor cost.

Model 1 Model 2

Area A 15 6

Area B 4 8

Area C 4 8

Revenue 90 65

Currently labor assignments provide for 10,000 hours in each of Areas A and B and 18000 hours in Area C. In addition, it is possible to transfer 2000 hours from area B to Area A. Similarly, 3000 hours may be transferred from area C to either Areas A or B. Develop the linear programming model to indicate how many of each model should be produced and how to allocate the workforce in order to maximize revenue.

5 Springmeadow Park Board is considering a new recreation complex with a variety of facilities. Expected costs (in thousands), space requirement (in square feet), and projected average usage figures are given in the table below. The department has a total of $1 million to spend specifically for the facilities. The building will have a maximum size of 20,000 square feet allocated to the indoor facilities listed below (thus this area excludes offices, lobbies, meeting rooms, etc.). In addition, there will be a maximum of 50,000 square feet of outdoor space available for these facilities. Councilman Bundy feels strongly that at most only one pool should be included in the complex. Councilwoman Simpson, whose daughter skates and son plays soccer, insists that if a baseball field is built then both a skating rink and soccer field must also be included in the park. If the park board wishes to maximize average usage of the complex, formulate the integer programming problem to determine which facilities should be included.

Facility Cost Space requirements Expected usage/day

Fitness Center (I) $200 2,000 60

Pool (I) 80 5,500 75

Pool (O) 65 7,200 40

Auditorium (I) 150 5,000 30

Gymnasium (I) 250 7,500 60

Tennis courts (O) 60 5,000 15

Baseball field (O) 90 25,000 35

Soccer fields (O) 80 25,000 44

Skating rink (I) 250 5,000 25

(I) indoor (O) outdoor

6. Assume Acme Inc is considering introducing a new product - super Deluxe Widgets. The Widgets will sell for $229 per unit. It is anticipated that the first year administrative costs will be $10,000 and the first year advertising budget is projected to be $8,000. The direct labor costs are uncertain, but it is believed they can be accurately can be represented by a normal distribution with a mean of $90 and a standard deviation of $30. Experts in the area have subjectively estimated the parts cost can be simulated by the discrete probability distribution listed below. The forecasted demand for the first year may be represented by a uniform distribution with limits of 500 and 700. Obtain summary statistics for 50 simulated trials to answer the four questions listed below. (Turn in the computer printout along with this answer sheet).

Cost per unit Probability

$60 .20

$65 .25

$70 .30

$75 .15

$80 .10

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