Reference no: EM133132268

Question 1. Equipment Acquisition. The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by trucks. The company has recently received a contract to begin supplying gasoline distributors in southern Ohio and has $300,000 available to spend on the necessary expansion of its fleet of gasoline tank trucks. Three models of gasoline tank truck are available:

			Monthly Operating
	Capacity	Purchase	Costs, Including
Truck Model	(gallons)	Cost	Depreciation

Super Tanker	5000	$37,000	$550
Regular Line	2500	$25,000	$425
Econo-Tanker	1000	$16,000	$350

The company estimates that the monthly demand for the region will be a total of 550,000 gallons of gasoline. Due to the size and speed differences of the trucks, the different truck models will vary in terms of the number of deliveries or round trips possible per month. Trip capacities are estimated at 15 per month for the Super Tanker, 20 per month for the Regular Line, and 25 per month for the Econo-Tanker. Based on maintenance and driver availability, the firm does not want to add more than 15 new vehicles to its fleet. In addition, the company would like to make sure it purchases at least three of the new Econo- Tankers to use on the short-run low-demand routes. As a final constraint, the company does not want more than half of the new models to be Super Tankers.
a. If the company wishes to satisfy the gasoline demand with a minimum monthly operating expense, how many models of each truck should be purchased?
b. If the company did not require at least three Econo-Tankers and allowed as many Super Tankers as needed, what would the company strategy be?

Note that the purchase cost of the tankers does not enter into the objective function (except as depreciation).

Question 2. Make or buy. The Carson Stapler Manufacturing company forecasts a 50000-unit demand for its Sure-Hold model during the next quarter. This stapler is assembled from three major components: base, staple cartridge, and handle. Until now Carson has manufactured all three components. However, the forecast of 50000 units is a new high in sales volume, and it is doubtful that the firm will have sufficient production capacity to make all the components. The company is considering contracting a local firm to produce at least some of the components. The production time requirements per unit are as follows:
                                                                                      Total Department
Department         Production Base     Time Cartridge    Handle     Time Available

A	0.03	0.02	0.05	400
B	0.04	0.02	0.04	400
C	0.02	0.03	0.01	400

Please note that in order to produce a part (base, cartridge, or handle) all three departments are required; however it is not necessary to internally produce all parts.

After considering the firm's overhead, material, and labor costs, the accounting department has determined the unit manufacturing coast for each component. These data, along with the purchase price quotations by the contracting firm, are as follows:

Component	Manufacturing Cost	Purchase Cost
Base	$0.75	$0.95
Cartridge	$0.40	$0.55
Handle	$1.10	$1.40

a. Determine the make-or-buy decision for Carson that will meet the 500000-unit demand at minimum total cost. How many units of each component should be made and how many purchased?

b. Which departments are limiting the manufacturing volume? If overtime could be considered at the additional cost of $3 per hour, which department(s) should be allocated the overtime? Explain.
c. Suppose that up to 80 hours of overtime can be scheduled in department A. What do you recommend?

Question 3. Pattern cutting. A firm has a work order for 500 sport jackets. A jacket is composed of 6 parts, left sleeve (LS), right sleeve (RS), left back (LB), right back (RB), left front (LF) and right front (RF). Each bolt of cloth, which costs $200, can be cut into one of the following patterns.
(1) 25 LB, 30 RF, ad 20 LF
(2) 20 RS, 10 RF, 10 RB and 15 LF
(3) 25 LS, 15 RS, 15 LB and 10 RB
(4) 30 RS, 10 LS, 10 LB and 20 LF

Set up and solve this problem. If each suit wholesales for $150. how much will the firm make? Note that one might get non-integer values for number of bolts using a particular pattern. That is ok for this exercise. For future reference, to insure integer values for Xi write @gin(Xi) after you have written all the other equations in the way you usually do; we will get back to this issue later in the course.

Question 4. Blending problem. Seastrand Oil Company produces two grades of gasoline: regular and high octane. Both types of gasoline are produced by blending two types of crude oil. Although both types of crude oil contain the two important ingredients required to produce both gasolines, the percentage of important ingredients in each type of crude oil differs, as well as the cost per gallon. The percentage of ingredients A and B in each type of crude oil, and the cost per gallon, are shown below:

Type of
Crude Oil   Cost          Ingredient A            Ingredient B

1	$0.10	20%	60%
2	$0.15	50%	30%

Each gallon of regular must contain at least 40% of A, whereas each gallon of high octane can contain at most 50% of B. Daily demand for regular octane gasoline is 800,000 gallons, and daily demand for high octane is 500,000 gallons. How many gallons of each type of crude oil should be used in regular and in high octane gasoline in order to satisfy daily demand at a minimum cost? Define the four decision variables as follows:

R1 = gallons of crude 1 used in regular gasoline

H1 = gallons of crude 1 used in high octane gasoline

R2 = gallons of crude 2 used in regular gasoline

H2 = gallons of crude 2 used in high octane gasoline

Question 5. The majestic Sprinkler Company buys ¾ inch schedule 40 PVC pipe which comes in 10 foot lengths and costs $12 per 10 foot length and cuts them into 30 inch, 42 inch and 56 inch lengths. The following is a list of required lengths for the next month. 1500 units of 30-inch pipe; 500 units of 42-inch pipe; and 600 units of 56-inch pipe. Any pipe length below 30- inches is considered waste. How many 10 foot lengths need to be purchased, what cutting patterns need to be used, and how many of each pipe will be produced if the firm is interested in minimizing the amount of money. Hint: first figure out the possible cutting patterns.

Question 6. Betsey Ross Dolls produces boy and girl dolls. The boy dolls sell for $8.00 and the Girl Dolls sell for $12.00, each. To make the dolls, the firm first produces a generalized human mold. The firm can produce 100 molds an hour and each mold can be used to produce either a boy or girl. The firm rents the mold making facilities and it costs $1,000 a week to rent and the facilities are open for 40 hours a week. The firm also rents the processing into gender facilities. There are two of them, each are open 40 hours a week. The first (A) can make 40 girl dolls an hour or 50 boy dolls per hour (or any combination in between), and cost $100 an hour to rent. The second (B) can make 20 girl dolls an hour or 30 boy dolls per hour (or any combination in between), and cost $70 an hour to rent. Solve for this week's production. Set up and solve via lingo. Do not worry about whole numbers.

Attachment:- Lingo solutions.rar