opm4 c

As with all Trident courses, you’re expected to provide references and citations.  It’s recommended you use the sources listed in the Module.  Resist the temptation to browse the Web, looking for “clues.”  There’s a lot of confusing stuff out there, and much of it is irrelevant.  This Module contains all the information you need.  Study it – use it! 

Case Assignment

The weight of each exercise, as a percent of the total Case grade, is given in parentheses following the exercise number. These weights are approximate: The details of grading are left to the discretion of the professor.

Problems 1 through 4 (5 points each): Define labels for the variables in the following situations, and write the constraints and profit functions in algebraic form.

Examples:

Ex 1. A dealer has the goal of selling at least 200 vehicles (cars plus trucks) each month. Write a constraint on car and truck sales.

Ex 1 Answer: Let

cars = number of cars sold per month

trucks = number of trucks sold per month

Then

cars + trucks >= 200

Ex 2. A bakery earns $1.00 for selling a dozen donuts, $1.50 for selling a dozen croissants, and $0.75 for selling a dozen bagels. Write their profit function.

Ex 2 Answer: Let

p = profit

donut = dozens of donuts sold,

crois = dozens of croissants sold

bagel = dozens of bagels sold

Then

p = 1(donut) + 1.5(crois) +0.75(bagel).

__________________

1. Filing cabinet A has a footprint (floor space requirement) of 4 square ft. Cabinet B has a footprint of 6 square feet. The office only has 30 square feet that can be used for cabinets. Write a constraint on the number of cabinets that should be installed.
2. An aid agency is buying generators for storm survivors. The resettlement area requires at least 15,000 kWh. Generator A is rated at 150 kWh, generator B is rated at 175 kWh. Write a constraint prescribing the number of generators of each type that can be purchased.
3. Larry’s Yard Care mows lawns, trims hedges and winterizes flower beds. The company charges $15 per hour for mowing, $12 per hour for trimming, and $25 per hour for winterizing. Write an hourly income function for the company, in terms of the number of jobs, by type, that were underway during that hour.
4. Thunder Garage assembles diesel engines for cars and trucks. The car engines have four cylinders, the truck engines have six. Each cylinder in a diesel engine requires a separate fuel injector. The supplier can only provide 1300 injectors per month. Write a constraint prescribing the number of each type engine that can be produced.
5. (30%):

All-Round Bakery is a small specialty business in downtown Los Angeles that makes only two products: powdered sugar donuts and chocolate glazed donuts. Their largest customer is the LAPD, which has a daily standing order for 100 dozen sugar donuts and 100 dozen chocolate donuts. Owing to storage and supply constraints, All-Round can only stockpile enough ingredients for 400 doz sugar donuts and 200 doz chocolate donuts per day. All-Round’s specialty machinery can bake 10 dozen donuts in a batch. The time required for a batch of sugar donuts is 10 minutes, or 1 minute per dozen. The time required for a batch of chocolate donuts is longer, owing to lower temperature. A batch of chocolate donuts requires 20 minutes, or 2 minutes per dozen. The machinery can operate a maximum of 10 hours (600 minutes) per day.

All-Round makes a profit of $1.75 on a dozen sugar donuts, and $2.00 on a dozen chocolate glaze donuts. How many dozen of each type should they bake daily, to maximize their profit?

The problem was solved using Waner’s (2010) simplex method tool. The output appears below, with the profit equation and constraints deleted. Work the problem yourself, check your solution against the correct solution, and provide the deleted information.

1. (50%):

Eye-Full Optics assembles astronomical telescopes, premium binoculars and student-grade microscopes from imported parts. Each telescope takes 1 hour to assemble, each pair of binoculars 2 hours, and each microscope 3 hours; the availability of skilled labor limits assembly work to 1000 hours per day. Eye-Full has a contract with FedEx, and must ship no less than 500 items per day. A contract with a major retailer requires them to deliver a minimum of 160 telescopes, 250 binocs, and 50 microscopes per day. But there are supply limitations. The telescopes and binocs are shipped with the same eyepieces; each scope has one, and each pair of binocs has two. The subcontractor who supplies the eyepieces can only furnish 800 per day. Similarly, both the binocs and the microscopes use the same prisms; each pair of binocs needs two, and each microscope needs four. The prism supplier can only ship Eye-Full 1400 per day.

If Eye-Full makes a profit on $100 on each scope, $200 on each pair of binocs, and $250 on each microscope, how many of each should the company manufacture each day? What is its optimum daily profit?

Solve the problem using an online app. Include either a screen shot of the output (preferred), or type the output. Be sure to include the profit function, the constraints, and the complete solution.

Assignment Expectations

• Graphics must be neat, clear and complete.  A graphics app can be used, but a freehand sketch is also acceptable. 
• All calculations should be shown. 
• All answers must be clearly stated.
• Relevant theory should be cited as necessary to explain which procedures were used to arrive at the answers, and why.
• Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online at https://mytlc.trident.edu/files/Writing-Guide_Trident_2014.pdf.
• There are no guidelines concerning length.  Write what you need to write – neither more, nor less.
• Clearly demonstrate your understanding of both the theory covered in the Module, and the particulars of the Case.
• Provide references and citations.  At a minimum, you should reference the course materials. These are referenced in APA format on the Background Info page.