MateCrown4619
1. A company manufactures two products: large fans and medium fans….
1. A company manufactures two products: large fans and medium fans. Each large fan requires 3 hours of wiring and 2 hours of drilling. Each medium fan requires 2 hours of wiring and 1 hour of drilling. There are 480 hours of wiring time available and 280 hours of drilling time available. Each large fan yields a profit of $30. Each medium fan yields a profit of $18. The company wants to manufacture at least 20 large fans. The objective is to maximize total profit.
(a) Formulate a linear optimization model for this problem by defining the decision variables, objective function and all the constraints. What do they represent?
(b) Find the optimal solution of this model by hand using the Corner Points graphical method.
2. Determine whether the following linear programming problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion.
Maximize 400x + 500y
Subject to
2x + 1y > 60
-3x + 4y < 90 x, y > 0
3. An air conditioning company manufactures three home air conditioners: a regular model, a super model, and a deluxe model. The profits per unit are $50, $85, and $105, respectively. The production requirements per unit and the availability of the three resources are given below:
Regular Model Super Model Deluxe Model Available
Number of fans 1 1 1 500
Number of cooling coils 1 3 5 1000
Manufacturing Time 12 22 25 6000 hours
How many regular models, super models, and deluxe models should the company manufacture in order to maximize profit?
(a) Formulate a linear optimization model for this problem by defining the decision variables, objective function and all the constraints. What do they represent?
(b) Solve this model by using the Excel Solver. Include Excel output with you answer.
(c) Determine the optimal solution. Interpret and make recommendations based on the optimal solution.
4. A real estate company is considering five possible projects: a small condominium complex, a small shopping center, a warehouse, a small business office building and a sports arena. Each of these projects requires different funding over the next three years, and the net present values of the projects also varies. The following table provides the required investment amounts (in $10,000s) and the net present value, NPV (in $10,000s), of each project:
PROJECT NPV YEAR 1 YEAR 2 YEAR 3
Condominium 210 64 60 58
Shopping center 200 50 45 58
Warehouse 160 50 32 60
Business Office Building 150 55 45 38
Sports Arena 185 50 44 40
The company has $2,600,000 to invest in year 1, $1,950,000 to invest in year 2 and $2,400,000 in year 3. The company wants to select at least 3 projects. In addition, the company also wants to select at least one project from the shopping center and sports arena projects.
(a) Formulate an integer optimization model for this problem to maximize the total profit in this situation by defining the decision variables, the objective function and all the constraints. What type of integer optimization model is this? Briefly describe what the objective function and each constraint represent.
(b) The optimal solution for the above problem is given below.
Variable values are X1 = 1, X2 = 1, X3 = 1, X4 = 0, X5 = 1.
The objective function value is 755.
Interpret the optimal solution to make a recommendation to the company.
