José and Maria are consulting for a firm in Seattle.

Test 1 DMT - (Spring 2012)

Instructions:

Format: Times New Roman, 12pts, 1.5” space, 1” margin (all around), Full Justification, English or Spanish, Name & Student Number on the upper right corner of first page, send it as a PDF file.

Don’t write the Question. Just your answers in a statement form, which can contain the Solver (or any other software that you use) solution.

All assumptions made, in each Situation, have to be included in the “statement form” (answer.)

Maximum of five pages.

Due Time: Sunday 22, 9:00PM. NO EXCEPTION. Those received after this time will receive an Incomplete.

Two or more tests that equitable resemble each other will receive zero.

When you send your test, write DMTTEST1 in the message subject.

Each violation of these instructions will have a 5% deduction, from the total scored.

Situation 1. Edda's Inc. is a producer of frozen pizza products. The company sells two kind of pizzas: Regular and Deluxe. Regular sells for $10 and cost $6 to produce, and Deluxe $15 and $9, respectively. Each week the firm has 70 pounds of dough mix, 25 pounds of topping mix, and $320 in its budget for producing both pizzas. Each Regular pizza uses 1 pound of dough mix and 4 ounces (16 ounces= 1 pound) of topping mix. Each Deluxe pizza uses 1 pound of dough mix and 6 ounces of topping mix. Based on past demand, Edda can sell at least 40 Regular pizzas and at least 35 Deluxe pizzas, each week. The problem is to determine the number of Regular and Deluxe pizzas the company should make to maximize net income.

Situation 2. R.T. produces two telephone models, each of which must go through three workstations for manufacturing, assembly, and quality control. At this time, the company is deciding between two Assembly processes, and only one of the Processes (1 or 2) will be used. The amount of time required for each model in each of the work areas is given in the following table.

Model Manufacturing Assembly Process 1

Assembly Process 2

Quality Control

Standard 7 minutes 5 minutes 2 minutes 2 minutes

Trimline 5 minutes 6 minutes 4 minutes 3 minutes

R.T. employs 11 workers, who each work a 7.5 hour day, and have been trained to work on any of the three processes. Accounting has stated that the cost of each Manufacturing minute is $0.95, each Assembly minute $0.25 or $0.35, respectively, depending which process is chosen, and each Quality Control minute $0.30, for a Standard Model. For the Trimline model, the costs are $0.25, $0.85 or $0.95 (Process 1 and 2), and $0.55. If R.T. sell for $7 the standard models and $10 the Trimline models, what should be the optimal daily production schedule. Situation 3. José and Maria are consulting for a firm in Seattle. They have two days off and want to go on a road trip to see the city of Denver. Their road atlas shows the driving time (in hours) between various city pairs, as shown below. Formulate (show the model) and solve a network model to find the quickest route to Denver.

Situation 4. The Polytechnic University of PR has received authorization from its President to hire up to 20 new full-time faculty members and spend up to $1,450,000 a year in new salaries. The school is seeking professors at all levels: assistant, associate,

and full professor. The dean of the school would prefer not to hire full professors. Accordingly, while the school may not seek faculty for all 20 positions, the dean has authorized that at least 50% of the new faculty who are hired should be assistant professors, and at least 70% of the new faculty hired should be below the rank of full professor. The respective departments within the school have convinced the dean, however, that at least three full professors should be hired to provide expertise in key areas. The following table gives the average salaries and years of experience for professors in each of the three ranks. The school is interested in hiring the most qualified mix of faculty (as measured by the total combined years of experience) that meets the university’s limitations and the dean’s authorizations.

Rank Average Salary Average Year of Experience

Assistant $55,003 2

Associate $69,885 7 Full $93,471 14

What is your analysis for the problem faced by the Faculty’s dean? Situation 5. The Tiny Timber Company wants to utilize best the wood resources in one of its forest regions. Within this region, there is a sawmill and a plywood mill. Thus, timber can be converted to lumber or plywood. Producing a marketable mix of 1000 board feet of lumber products requires 1000 board feet of spruce and 4000 board feet of Douglas fir. Producing 1000 square feet of plywood requires 2000 board feet of spruce and 4000 board feet of Douglas fir. This region has available 32,000 board feet of spruce and 72,000 board feet of Douglas fir. Sales commitments require at least 5000 board feet of lumber and 12,000 square feet of plywood be produced during the planning period. The profit contributions arc $45 per 1000 board feet of lumber products and $60 per 1000 square feet of plywood. Let L be the amount (in 1000 board feet) of lumber produced and let P be the amount (in 1000 square· feet) of plywood produced. Express the problem as a linear programming model.

Situation 6. PRComputers makes quarterly decisions about their product mix. While their full product line includes hundreds of products, we will consider a simpler problem with just two products: notebook computers and desktop computers. PRComputers would like to know how many of each product to produce in order to maximizes profit for the quarter. There are a number of limits on what PRComputers can produce. The major constraints are as follows:

o Each computer (either notebook or desktop) requires a Processing Chip. Due to tightness in the market, our supplier has allocated 10,000 such chips to us.

o Each computer requires memory. Memory comes in 16MB chip sets. A notebook computer has 16MB memory installed (so needs 1 chip set) while a desktop computer has 32MB (so requires 2 chip sets). We received a great deal on chip sets, so have a stock of 15,000 chip sets to use over the next quarter.

o Each computer requires assembly time. Due to tight tolerances, a notebook computer takes more time to assemble: 5 minutes versus 3 minutes for a desktop.

o There are 20,000 minutes of assembly time available in the next quarter. Given current market conditions, material cost, and our production system, each notebook computer produced generates $210 profit, and each desktop produces $300 profit.

There are many questions PRComputer might ask. The most obvious are such things as “How many of each type computer should PRComputer produce in the next quarter?", “What is the maximum profit PRComputer can make?" Less obvious, but perhaps of more managerial interest is “How much should PRComputer be willing to pay for an extra memory chip set?" “What is the effect of losing 1,000 minutes of assembly time due to an unexpected machine failure?", “How much profit would we need to make on a 32MB notebook computer to justify its production?". What do you suggest? Situation 7. Carmen, the manager of a department store in Puerto Rico, is attempting to decide on the types and amounts of advertising the store should use. She has invited representatives from a local radio station, a television station, and a newspaper to make presentations in which they describe their audiences. The

television station representative indicates that a TV commercial, which costs $20,000 per spot, would reach 35,000 potential customers. The newspaper representative claims to be able to provide an audience of 10,000 potential customers at a cost of $4,000 per ad. The radio station representative says that the audience for one of the station’s commercials, which costs $5,000 per spot, is 15,000 customers. The breakdown of the audience (in thousands) is as follows.

Television Newspaper Radio

Male Female Male Female Male Female Senior 5 5 4 3 1.5 1.5

Young 5 10 2 1 4.5 7.5

The store has the following advertising policy:  Use at least twice as many radio commercials spots as newspaper ads and

TV commercial spots, combined.  Reach at least 120,000 customers.  Reach at least twice as many young people as senior citizens.  Make sure that at least 25% of the total audience is female.

Available space limits the number of newspaper ads to seven. Carmen wants to know the optimal number of each type of advertising to purchase.