Reference no: EM133148437
1. The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability:
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Product (hours/unit)
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|
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Department
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1
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2
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Labor-Hours Available
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A
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1.00
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0.35
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100
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B
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0.30
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0.20
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36
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|
C
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0.20
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0.50
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50
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Profit contribution/unit
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$30.00
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$15.00
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|
a. Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products 1 and 2.
b. In computing the profit contribution per unit, management doesn't deduct labor costs because they are considered fixed for the upcoming planning period. However, sup- pose that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime? How much would you be willing to pay per hour of overtime in each department?
c. Suppose that 10, 6, and 8 hours of overtime may be scheduled in departments A, B, and C, respectively. The cost per hour of overtime is $18 in department A, $22.50 in department B, and $12 in department C. Formulate a linear programming model that can be used to determine the optimal production quantities if overtime is made avail- able. What are the optimal production quantities, and what is the revised total contribution to profit? How much overtime do you recommend using in each department? What is the increase in the total contribution to profit if overtime is used?
18. The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by truck. The company recently contracted to supply gasoline distributors in southern Ohio, and it has $600,000 available to spend on the necessary expansion of its fleet of gasoline tank trucks. Three models of gasoline tank trucks are available.
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Truck Model
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Capacity (gallons)
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Purchase Cost
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Monthly Operation Cost, Including Depreciation
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Super Tanker
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5000
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$67,000
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$550
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Regular line
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2500
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$55,000
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4425
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Econo-Tanker
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1000
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$46,000
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$350
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The company estimates that the monthly demand for the region will be 550,000 gallons of gasoline. Because of the size and speed differences of the trucks, the number of deliveries or round trips possible per month for each truck model will vary. Trip capacities are esti- mated at 15 trips per month for the Super Tanker, 20 trips per month for the Regular Line, and 25 trips per month for the Econo-Tanker. Based on maintenance and driver availabil- ity, the firm does not want to add more than 15 new vehicles to its fleet. In addition, the company has decided to purchase at least three of the new Econo-Tankers for use on short- run, low-demand routes. As a final constraint, the company does not want more than half the new models to be Super Tankers.
a. If the company wishes to satisfy the gasoline demand with a minimum monthly oper- ating expense, how many models of each truck should be purchased?
b. If the company did not require at least three Econo-Tankers and did not limit the num- ber of Super Tankers to at most half the new models, how many models of each truck should be purchased
21. Star Power Company is a power company in the Midwest region of the United States. Star buys and sells energy on the spot market. Star can store power in a high-capacity battery that can store up to 60 kWh (kilowatt hours). During a particular period, Star can buy or sell electricity at the market price known as LMP (Locational Marginal Price). The maxi- mum rate that power can be injected or withdrawn from the battery is 20 kWh per period. Star has forecasted the following LMP's for the next 10 periods:
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Period
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LMP ($/kWh)
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1
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$5
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2
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427
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3
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$2
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4
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$25
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|
5
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$22
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|
6
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$29
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|
7
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$24
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|
8
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$20
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9
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$61
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10
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$66
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The battery is full at the beginning of period 1; that is, at the start of the planning horizon, the battery contains 60 kWh of electricity.
a. Develop a linear programming model Star Power can use to determine when to buy and sell electricity in order to maximize profit over these 10 weeks. What is the maximum achievable profit?
b. Your solution to part (a) should result in a battery level of 0 at the end of period 10. Why does this make sense? Modify your model with the requirement that the battery should be full (60 kWh) at the end of period 10. How does this impact the optimal profit?
c. To further investigate the impact of requirements on the battery level at the end of period 10, solve your model from part (b) with the constraint on the ending battery level varying from 0 kWh to 60 kWh in increments of 10 kWh. Develop a graph with profit on the vertical axis and required ending battery level on the horizontal axis. Given that Star has not forecasted LMPs for periods 11, 12, and so on, what ending battery level do you recommend that Star use in its optimization model?