Reference no: EM133016163

Problem #1 (Developing Linear Optimization Models): Valencia Products makes automobile radar detectors and assembles two models: LaserStop and SpeedBuster. The firm can sell all it produces. Both models use the same electronic components. Two of these can be obtained only from a single supplier. For the next month, the supply of these is limited to 4,000 of component A and 3,500 of component B. The number of each components required for each product and the profit per unit are given in the table:
Components Required per Unit
Product A B Profit/Unit
LaserStop 18 6 $124
SpeedBuster 12 8 $136

Part a: identify the decision variables, objective function, and constraints in simple verbal statements.

Part b: mathematically formulate a linear optimization model.

Problem #2 (Developing Linear Optimization Models): A brand manager for ColPal Products must determine how much time to allocate between radio and television advertising during the next month. Market research has provided estimates of the audience exposure for each minute of advertising in each medium, which it would like to maximize. Costs per minute of advertising are also known, and the manager has a limited budget of $25,000. The manager had decided that because television ads have been found to be more effective than radio ads, at least 75% of the time should be allocated to television.

Part a: identify the decision variables, objective function, and constraints in simple verbal statements.

Part b: mathematically formulate a linear optimization model.

Problem #3 (Developing Linear Optimization Models): A business student has $2,500 available from a summer job and has identified three potential stocks in which to invest. The cost per share and expected return over the next two years is given in this table:

Stock A B C
Price/share $12 $15 $30
Return/share $8 $7 $11

Part a: identify the decision variables, objective function, and constraints in simple verbal statements.

Part b: mathematically formulate a linear optimization model.

Problem #4 (Solving Linear Optimization Models): Implement the linear optimization model that you developed for Valencia Products in Problem #4 on a spreadsheet and use Solver to find an optimal solution. Interpret the Solver Answer Report, identify the binding constraints, and verify the values of the slack variables by substituting the optimal solution into the model constraints.

Problem #5 (Solving Linear Optimization Models): Implement the linear optimization model that you developed for the investment scenario in Problem #7 on a spreadsheet and use Solver to find an optimal solution. Interpret the Solver Answer Report, identify the binding constraints, and verify the values of the slack variables by substituting the optimal solution into the model constraints.

Problem #6 (How Solver Works): For the Valencia Products model in Problem #4, graph the constraints and identify the feasible region. Then identify each of the corner points and show how increasing the objective function value identifies the optimal solution.

Problem #7 (How Solver Works): For the ColPal model in Problem #5, graph the constraints and identify the feasible region. Then identify each of the corner points and show how increasing the objective function value identifies the optimal solution.

Problem #8 (Integer Linear Optimization Models): Solve the following problem (which is #12 from Chapter 13) ensuring the number of units produced is an integer. How much difference is there between the optimal integer solution objective function and the linear optimization solution objective function? Would rounding the continuous solution have provided the optimal integer solution?