TOYCO assembles three types of toys - trains, trucks, and cars - using three operations, named OP1, OP2, and OP3. The daily time availabilities for the three operations are as follows: 418 minutes for OP1, 382 minutes for OP2, and 461 minutes for OP3. The revenues per unit of train, truck, and car toys are 34.2 USD, 15.1 USD, and 50.3 USD, respectively. The assembly times (in minutes) needed per unit toy are indicated below: One train requires 1.5 minutes of assembly for OP1, 2.1 minutes of assembly for OP2, and 1 minutes of assembly for OP3. One truck requires 3.4 minutes of assembly for OP1 and 24 minutes of assembly for OP3 (trucks do not require OP2). One car requires 1.1 minutes of assembly for OP1 and 4.4 minutes of assembly for OP 2 (cars do not require OP3). TOYCO would like to determine the numbers of each type of toys produced so that the total daily revenues are maximized. (a) (4 points) Define clearly the decision variables of the problem. (Hint: 3 variables are needed!) (b) (4 points) Express the model's objective. (c) (8 points) Express the model's constraints. (d) (8 points) Build an Excel sheet corresponding to your model and solve the linear pro- gramming problem using Excel's Solver. Ignore the fact that the solution needs to be integer. Report the optimal solution (production mix) obtained Round the optimal so- lution to two digit places if necessary, Note: You need to submit your Excel sheet along with your answer. (e) (4 points) Report the optimal total daily revenue generated by TOYCO. Round the amount to the cent if necessary (0.7 points) Get the shadow prices of the three resources (assembly minutes for each op- eration) from the sensitivity report and interpret them economically. Round the shadow prices to the cent if necessary. (9) (7 points) Get the optimality ranges (allowable increase and descrease) of the three variables (first part of the sensitivity report) and provide an interpretation. Round the allowable increase and the allowable decrease to two digit places if necessary. TOYCO assembles three types of toys - trains, trucks, and cars - using three operations, named OP1, OP2, and OP3. The daily time availabilities for the three operations are as follows: 418 minutes for OP1, 382 minutes for OP2, and 461 minutes for OP3. The revenues per unit of train, truck, and car toys are 34.2 USD, 15.1 USD, and 50.3 USD, respectively. The assembly times (in minutes) needed per unit toy are indicated below: One train requires 1.5 minutes of assembly for OP1, 2.1 minutes of assembly for OP2, and 1 minutes of assembly for OP3. One truck requires 3.4 minutes of assembly for OP1 and 24 minutes of assembly for OP3 (trucks do not require OP2). One car requires 1.1 minutes of assembly for OP1 and 4.4 minutes of assembly for OP 2 (cars do not require OP3). TOYCO would like to determine the numbers of each type of toys produced so that the total daily revenues are maximized. (a) (4 points) Define clearly the decision variables of the problem. (Hint: 3 variables are needed!) (b) (4 points) Express the model's objective. (c) (8 points) Express the model's constraints. (d) (8 points) Build an Excel sheet corresponding to your model and solve the linear pro- gramming problem using Excel's Solver. Ignore the fact that the solution needs to be integer. Report the optimal solution (production mix) obtained Round the optimal so- lution to two digit places if necessary, Note: You need to submit your Excel sheet along with your answer. (e) (4 points) Report the optimal total daily revenue generated by TOYCO. Round the amount to the cent if necessary (0.7 points) Get the shadow prices of the three resources (assembly minutes for each op- eration) from the sensitivity report and interpret them economically. Round the shadow prices to the cent if necessary. (9) (7 points) Get the optimality ranges (allowable increase and descrease) of the three variables (first part of the sensitivity report) and provide an interpretation. Round the allowable increase and the allowable decrease to two digit places if necessary
