1. J. Sells the dietician at Kalous Hospital must prepare a breakfast menu for patients with Lazzari's Disease. The table below summarizes the relevant data per ounce for each of the three food groups. The meal must consist of at least 10 ounces. Lazzari's patients require high Vitamin A low Vitamin B diets. Thus the diet must contain at least 20% Vitamin A and no more than 10% Vitamin B. At least 20 percent of the calories should come from cereals. Formulate the LP model to minimize cost.
Cost
per ounce Vitamin A Vitamin B Calories
Eggs $0.50 10% 10% 60
Bacon Strips $0.90 30% 20% 120
Cereal $0.20 15% 5% 90
Objective function: ______________________________________________
ST.
2. Lakeside Boatworks is planning the production of their fiberglass recreational boats for the next four months. The forecasted demand is 450 for April, 420 for May, 450 for June and 500 for July. The production capacity is 470, 450, 380 and 470 for April, May, June and July respectively. The projected production costs are $7,000 for April, $8,000 for May, and $9,000 for June and July. Boats that are not sold in the months in which they are produced can be put into storage for sale during the following months. Each month, the inventory costs are $50 per boat. A maximum of 70 boats can be put into storage at the end of each month. It is possible to use overtime labor in April to produce an additional 50 boats at a cost of $7,500 per boat. Formulate the LP model to minimize production and inventory costs and meet the demand for the next four months.
Objective function: ______________________________________________
ST.
3. At the end of each week, General Appliance ships (by truck) refrigerators that they produce in plants located in Atlanta and Boston to distribution centers located in Chicago, Denver, and Eugene. Relevant shipping costs are presented in the table below. The route from Boston to Eugene is serviced by only one truck and is therefore limited to 50 units shipped per week on this route. In addition, refrigerators can be sent from the distribution center in Chicago to Denver at a cost of $30 per unit. Finally, it is possible to ship refrigerators by freight from Boston to Eugene for a price of $80 per unit, but only if the weekly shipment amount is exactly 200 units per week. Formulate the LP model to minimize weekly shipping cost.
Distribution Centers
Plants Chicago Denver Eugene Supply
Atlanta $40 $65 $120 500
Boston $50 $60 $130 400
Demand 300 300 300
Objective function: ______________________________________________
ST.
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