## (solution) QBA 775 Assignment #2 Name _________________________ Due during

QBA 775 Assignment            #2                    Name _________________________

Due during final exam period

1. Wheeler?s Containers has agreed to terms with Mountain Dew to produce 100,000 twelve ounce aluminum cans for their soda during the next month.  The cans are stamped from aluminum sheets.  A can consists of a main body (rectangular stamp) and two ends (a round stamp). Wheeler?s has identified 4 possible stamping patterns (involving 2 different types (sizes) of aluminum sheets) as shown below.  The table below summarizes the relevant information on the four patterns.  They have 130,000 minutes of stamping time available and 50,000 Regulars sheets of aluminum (an unlimited number of large sheets).  Formulate the LP model to meet the agreed upon terms and minimize the scrap.  (10 points).

Pattern 1              Pattern 2      Pattern 3          Pattern 4

Type of Sheet                             Regular                 Large            Regular               Regular

Time to Stamp (minutes)                   2                        4                      2                      4

Amount of Scrap                              4                        8                      7                      3

1a. how many Regular sheets will be cut according to Pattern 3?__0______

1b. Which constraints are binding? ____The ratio of circular ends to the rectangular disk is 2:1 and the total number of cans should be equal to 10000______

1c. What would be the total scrap if 135,000 Regular sheets were available? ___233,333___

1d. How many minutes will be used to obtain the optimal solution?

__129999.86 min_______

2.   Assume you have just been hired by Sandpiper Airlines.  Your first assignment with Sandpiper is to determine the optimal load for cargo planes.  Sandpiper transports products from Boston to an exclusive remote village on the Eastern seaboard.  The products transported include crates of Widgets, Gadgets, and Thingamagigs.   Your job is to determine how many crates of each of the three products should be loaded on each cargo flight in order to maximize revenue.  The cargo plane has two storage compartments, one in the rear of the plane and one in the front of the plane.  You have determined that the storage size for the front compartment is equal to 600 and the size of the rear storage is 800.  To ensure that the plane does not flip over in mid-flight, the weight in the rear should be twice as much as the weight in the front storage.  Of course, all exclusive villages on the Eastern seaboard must have plenty of Thingamagigs.  Thus, Sandpiper?s contract guarantees at least 25 percent of the products transported on each flight will be Thingamagigs. Information on the three products is presented in the table below.   Formulate the LP model to maximize revenue.

Products

Revenue / crate           15                    30                                50

Size / crate                   2                     4                                 8

Weight / crate              6                     4                                 8

2a. How many crates of Thingamagigss should be loaded on each flight? ______95____

2b. Which constraints are binding? _____two; size and weight_____________

2c. What would be the maximum revenue if the size of the front storage was equal to

700?

___9625____

2d. What would be the maximum revenue if the size of the rear storage was equal to

750?

____9225 given front storage size was 600_____

2e. How many total product (all three together) will be loaded in the rear storage?___117.5 meaning either 117 or 118 given rear size = 800 and front size = 600___

3. Phil?s Tennis Emporium Club has three indoor tennis courts.  Phil is perplexed about how much time to set aside for each of the six revenue producing activities listed in the table below.  The Club in open from noon to 10 PM Tuesday through Sunday (i.e, each of the three courts is available for 10 hours per day, six days per week).  To satisfy club members, Phil has decided that at least one-half(1/2) of the available court time each week must be set aside for individual members play.  A session for individual members takes up one hour of court time and produces \$10 revenue as shown in the table below.  Individual lessons by the head tennis pro, M. Hall, requires one hour and generates \$30 revenue, while individual lessons by the assistant pro, D. Martin, requires one hour of court time and generates \$25 revenue.  M. Hall and D. Martin work together during each group sessions (i.e., both are present during an adult group lesson and both are present during a youth group lesson).  Head pro M. Hall is only willing to work 30 hours per week, while assistant pro D. Martin is willing to work up to 40 hours per week.  Phil believes that Youth Group Lessons is an effective method to build membership in the club.  Therefore Phil has decided to set aside at least 20 hours per week to schedule Youth Group Lessons.  Determine how many sessions of each of the six activities should be scheduled per week in order to maximize Phil?s weekly revenue.

*The specific dates and times of the activities do not need to be addressed in this formulation.

Activity                                   Court hours per session        Revenue per session

Individual member play                      1 hour                                      \$10

League Play                                        5 hours                                                \$50

Individual Lesson (head pro)              1 hour                                      \$30

Individual Lesson (assistant pro)        1 hour                                      \$25

Group Lesson ? Adults                       2 hours                                                \$120

Group Lesson ? Youth                       2 hours                                                \$100

3a. How many of each type of activity should be scheduled per week? __________Adults only 30 sessions per week__

3b. Some individual lessons by the head pro would be scheduled if the revenue was equal to what value?

_______No value. Individual lessoons would not be scheduled____

3c. What would be the weekly revenue if the Head Pro was willing to work 35 hours per week?

________2550 if he works 35 hours no more no less, but 3600 if he works at most 35 hrs per week_

3d. What would be the maximum revenue if the Assistant Pro was only willing to work 35 hours per week?

_____2375________

4. Inferior Tile produces square vinyl floor tile is three sizes, small (8 X 8), medium (12X12) and large (16 X 16).  The tile produced on three machines that vary in terms of the width of the tile produced.  Machine 1 produces tile that is 12 inches wide, machine 2 produces tile that is 16 inches wide, and machine 3 produces tile that is 24 inches wide.  The small tile can be produced on any one of the three machines, however there will be waste when Machine 1 is used.  That is, the width of the tile will be 8 inches, leaving 4 inches of waste.  There will be no waste on the other to machines since 2 smalls (8 X 8) produced on machine 2 will 16 inches wide and three tiles produced on machine 3 will be 24 inches wide.  The same logic applies to medium and large tiles.  The forecasted demand for the following production period is to produce 9,600 small, 11,200 medium and 4,200 large tile squares.  The machines have a limited capacity and the time required in minutes to cut each tile varies on the machine as shown in the table below.

*An 8X16 inch tile from machine 3 cannot be cut in half and is considered 8 inch waste.

Time in minutes (machine 3 can cut three 8X8 tiles in 30 seconds).

Machine 1                Machine 2            Machine 3

Small                     .2                           .4                     .5

Medium                 .3                           .3                     .6

Large                     N/A                       .4                     .5

Time available      35 hrs                     35 hrs              40 hrs

Formulate the LP model to determine how many tile should be cut on each machine and meet the forecasted demand and minimize waste.

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Sep 13, 2020

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