Instructions:

• Build Optimization Models to solve this homework.
• Explain your answer and reasoning clearly.
• You may work in groups, but write/type your own homework report.
• Upload your Excel file unto BlackBoard.

Problem 1:

Howie Jones owns and operates Blue Ridge Hot Tubs, a company that sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie purchases prefabricated fiberglass hot tub shells and installs common water pumps and the appropriate amount of tubing into each hot tub. Every Aqua-Spa requires a pump, 12 hours of labor and 16 feet of tubing; every Hydro-Lux requires 2 pumps, 16 hours of labor and 8 feet of tubing. Demand for these products is such that each Aqua-Spa produced can be sold to generate a profit of $275, and each Hydro-Lux produced can be sold to generate a profit of $250. The company expects to have 450 pumps, 91 workers, and 3,080 feet of tubing available during the next weeks production cycle. Determine the optimal number of Aqua-Spas and Hydro-Luxes to produce to maximize profit assuming all employees work their 40 hours with no overtime.

1. What are the objective function, decision variables, and constraints for this optimization problem?
2. Develop an Excel spreadsheet and use Excel-Solver to find an optimal solution for this problem.
3. Describe the optimal solution in words.

Problem 2:

A company has three manufacturing plants (in Atlanta, Tulsa, and Springfield) that produce a product that is then shipped to one of four distribution centers A, B, C, or D. The three plants can produce 15, 22, and 15 truckloads of product each week, respectively. Distribution centers A & B need 12 truckloads of product each week and Distribution centers C & D need 13 truckloads of product each week. The shipping costs per truckload between the plants and distribution centers are given in the table. The company needs to determine how much to ship from each plant to each distribution center, and would like to minimize total shipping costs.

	Distribution Center
Plant	A	B	C	D
Atlanta	$ 800	$1300	$400	$ 700
Tulsa	$1100	$1400	$600	$1000
Springfield	$ 600	$1200	$800	$ 900

1. What are the objective function, decision variables, and constraints for this optimization problem?
2. Develop an Excel spreadsheet and use Excel-Solver to find an optimal solution for this problem.
3. Describe the optimal solution in words.

D 1 2 A B D Blue Ridge Hot Tubs Decision Variables Aqua-Spa Hydro-Lux X X2 Quantity Profit/Tub 275 250 Resource per Aqua-Spa Hydro-Lux 1 2 12 16 16 8 Constraints Resource pumps labor tubing LHS: Resource Used F Objective Value G RHS: Resource Type: Available