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The Limewood Furniture Company produces tables and chairs from two resources: labor and wood. The company has 80 hours of labor and 34 pounds of wood...

The Limewood Furniture Company produces tables and chairs from two resources: labor and wood. The company has 80 hours of labor and 34 pounds of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 pounds of wood to produce, whereas a table requires 10 hours of labor and 7 pounds of wood. The profit from each chair is $350 and from each table is $150. The company wants to determine the number of chairs and tables to produce to maximize profit.

a. Formulate a linear programming model for this problem.
b. Solve this model using graphical analysis.


A restaurant sells ice cream and frozen yogurt. The restaurant makes one order for ice cream and frozen yogurt per week, and the store has enough freezer space for 110 gallons of both products. A gallon of frozen yogurt costs $ 0.85 and a gallon of ice cream costs $0.95, and the restaurant budgets $90 each week for these products. The manager estimates that each week the restaurant sells at least twice as much ice cream as frozen yogurt. Profit per gallon of ice cream is $4.30 and profit per gallon of frozen yogurt is $3.90.

a. Formulate a linear programming model for this problem.
b. Solve this model using graphical analysis.

The Collins family owns 405 acres of farmland in NC on which they grow corn and tobacco. Each acre of corn costs $110 to plan, cultivate, and harvest; each acre of tobacco costs $215. The Collins budget $55,000 for next year. The government wants to limit the number of acres of tobacco that can be planted to 100 acres. The profit for each acre of corn is $325; the profit from each acre of tobacco is $525. How many acres of each crop should be planted in order to maximize profit?

a) Formulate a linear programming model and solve.
b) How many acres of farmland will not be cultivated at the optimal solution? Do the Collins use the entire 100 acre tobacco allotment?
c) What would the profit for corn have to be for the Collins to plant only corn?
d) If the Collins can obtain an additional 100 acres of land, will the number of acres of corn and tobacco they plan to grow change?
e) If they decide not to cultivate a 50 acre section as part of a crop recovery-program, how will it affect their crop plans?

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