ISDS 361BTest 2

Dr. Chen Sample

Last Name / First Name / Station No.
Problem / Maximum Score / Your Score / Worksheet
1 / 15
2 / 30
3 / 20
4 / 10
5 / 25
TOTAL / 100

Problem 1 (15 Points):

S&S Toy Company produces two dolls that are popular with young girls, the male Jack doll and the female Jill doll. Both dolls are made from plastic and come with a variety of outfits in standard packages.

  • The Jack doll requires 5 ounces of plastic as compared to 3 ounces for the Jill doll.
  • The Jill doll uses 2 linear feet of cloth as compared to 1 linear foot of cloth of clothes packaged with the Jack doll.
  • There are 8000 linear feet of cloth for clothesavailable each week
  • There are 600 pounds of plastic each week available each week
  • They have a total production time to make at most 3000 dolls each week
  • The Jill doll is priced to net a unit profit of $7 on each doll while each Jack doll nets a profit of $5.
  • The goal is to maximize total profit

A.Write a linear program to represent to above situation:

Decision Variable:

Objective Function:

Constraints:

B. The optimal solution

Number of Jack Dolls should they manufacture per week
Number of Jill Dolls should they manufacture per week
Expected profit per week

Problem 2 (30 Points)

Howard Manufacturing produces five major appliances – stove, washers, electric dryers, gas dryer, and refrigerators. All products go through three processes – molding/pressing, assembly, and packaging.

  • Each week there are 5600 minutes available for molding/pressing, 3000 available for packaging, 1200 for stove assembly, 1200 for refrigerator assembly, and 2800 that can be used for assembling washers and dryers.
  • The table below gives the gross unit net profit that includes the material and labor as well as the molding/pressing, assembly and packaging times (in minutes) required for the production of each type of appliance:
  • Howard will like the number of washers to be equal the combined number of dryers.
  • The number of electric dryers should not exceed the number of gas dryers by more than 100 per week

A Linear Programming model is formulated as follows:

Solution of the above LP yields an optional production schedule with total profit of $92,166.67 and the sensitivity report is depicted as follows:

  1. Will you present the production schedule to the management even if the optimal solution has fraction number? (for example number of stove = 123.45)

  1. Suppose the net profit of electric dryer is $110, will you recommend produce electric dryer? Why?
  1. Suppose the assembly time for washer and dryer costs you $10 per minute now, how much should Howard be willing to pay for an extra hour of washer and dryer’s assembly time?Discuss for how many minutes your statement above is valid.
  1. Suppose the molding/pressing time for washer and dryer costs you $12 per minute now, how much should Howard be willing to pay for 100 extra minutes of molding/pressing time?
  1. Would the optimal schedule changes if Howard underestimates the profit of stove by $10? Why or why not?
  1. Suppose that the number of washer and dryers combined should not exceed more than 50% of the total production. Using a definitional variable write the appropriate constraints that would modify your model. You do not have to re-solve the model

Problem 3 (20 points)

Clancy’s Casino, in Muledeer, Nevada, is open 24 hours a day, seven days a week. Along with all the other attractions and diversion, Clancy’s operates a variety of gaming tables. Dealers at these tables are interchangeable. The casino has the following daily requirements for dealers:

ShiftTime BlockMinimum # of Dealers Needed

10100 – 05007

20500 – 09004

30900 – 13009

41300 – 170012

51700 – 210015

62100 – 010017

A dealer may start work at the beginning of any one of the six shifts and, having begun, works eight consecutive hours.

A. Find the employee schedule that minimizes the total number of dealers required, meeting the minimum level of each shift’s requirements.

  1. Suppose Clancy’s Casino pays a wage differential depending on the hours worked. In particular,
  • between midnight and 0700, it pays dealers $16 per hour,
  • between 0700 and 1900 $10 per hour,
  • and between 1900 and midnight $12 per hour.

Modify your objective function to part A to determine a schedule for Clancy’s so that the total wage is minimum (Just list the revised objective function)

Problem 4 (10 Points)

BridgeCity Developers is coordinating the construction of an office complex. As part of the planning process, the company generated the following simplified activity list:

  1. Identify the critical path
  1. How long will it take to complete the project?
  1. Can activity B be delayed without delaying the entire project? If so, by how many weeks?

Problem 5 (25 Points)

Trey Taylor is in charge of planning and coordinating next spring’s sales management training program for MBI Corporation. Trey has listed the following activity information for this project:

a)What is the expected completion time in weeks for this project?

b)If Trey can not complete the project within 16 weeks, MBI has to turn over the training project to Titan Sales Training Institute which charges $200,000. MBI has three options:

Option 1:

Do nothing

Option 2:

For $10,000, MBI can outsource a local advertising company Happy Ad to prepare and mail brochure. Happy Ad is certain that they can prepare and mail brochure in exactly 2 weeks

Option 3:

Trey can hire a temporary assistant for $1,000 to help himtake reservation. This will cut three time estimates for that activity by 10% each.

Which option will you recommend and show expected valued for each option:

Option 1
Option 2
Option 3

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