Steelco manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the furnaces at each mill, the time and cost to produce a ton of steel differs for each mill. The time and cost for each mill are shown in the table below. Each month, Steelco must manufacture at least 500 tons of steel 1 and 600 tons of steel 2. Formulate an LP to minimize the cost of manufacturing the desired steel.

4 A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units H and software programs S is given by TC=aH+bS−cHS   For the​ product-specific case for​ software, the firm experiences

A call center has 60 employees on‐line, each of whom make one phone call every 3 min on average, and talk on average for 2 min. Each call costs 15¢. What is the total traffic in erlangs? How many circuits are required for a GoS of 1%? How much should the yearly (250 working days, 8 working hours a day) lease price be for the company to make a 50% saving in its telephone bills over the first 3 years? Assume the lease set‐up fee of $30,000 should be paid over a period of 3 years.

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Truckco manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled; if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes $300 to profit; each Type 2 truck contributes $500. How much capacity in percent does a single truck of each type uses at each shop?

Clyde Clerk is reviewing his firm’s expense reimbursement policies with the new salesperson, Trav Farr. “Our reimbursement policies depend on the situation. You see, first we determine if it is a local trip. If it is, we only pay mileage of 45 cents a mile. If the trip was a one-day trip, we pay mileage and then check the times of departure and return. To be reimbursed for breakfast, you must leave by 7:00 A.M., lunch by 11:00 A.M., and have dinner by 5:00 P.M. To receive reimbursement for breakfast, you must return later than 10:00 A.M., lunch later than 2:00 P.M., and have dinner by 7:00 P.M. On a trip lasting more than one day, we allow hotel, taxi, and airfare, as well as meal allowances. The same times apply for meal expenses.” Draw a decision tree depicting the reimbursement policy in this Problem using LucidChart or Word document

A coal mine purchased 3 years ago for $7 million was estimated to contain 4,000,000 tons of coal. During the past 3 years the amount of coal removed was 21,000, 18,000, and 20,000 tons, respectively. The gross income obtained in these 3 years was $257,000 for the first year, $320,000 for the second year, and $340,000 for the third year. What is the cost depletion allowance for year 1.

Sprocket manufacturing. The manager of this production firm is faced with a potential problem: shortages in the supply of a vital gear sprocket. He is considering the development of an in-house capability to make the sprockets, knowing that the firm needs 35,000 such sprockets each year. If the firm elects to make the sprockets internally, then it must select one of the three possible production processes. Each has different costs, as shown in Table 10.17. Adopting a manual process may lead to union problems. The manager estimates the probability of these problems as 25%, and knows that if they do occur, then the variable cost will increase by $0.50 per sprocket. Further, if the semi-automatic or fully automatic option is selected, then additional training of personnel will be required. The amount and therefore the cost of training are uncertain. For the semi-automatic process, the fixed cost of basic training will add $15,000. However, there is a 20% chance the workers will need extra…

Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk. His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio maximizes the expected return but provides an annual return of no less than 3%. for each of the following scenarios. Annual Returns (Planning Scenarios): mutual fund yr 1 yr 2 yr 3 yr 4 international stock 22.37 26.73 6.46 -3.19 low-cap blend 14.88 18.61 10.52 5.25 mid-cap blend 19.45 18.04 5.91 -1.94 small-cap blend 13.79 11.33 -2.07 6.85 intermediate bond 7.29 8.05 9.18 3.92 Formulate the appropriate linear program for this situation. (state the objective function, the decision variables, and the constraints)