The Williams Novelty Company makes stuffed animals. Production for the remaining week in the fiscal year is to be set to make use of existing raw material inventory and contracted labor while maximizing profit and making at least 100 animals. The following table indicates the total availability of fabric, assembly hours, and trim as well as the per animal requirements for each. For example, each stuffed bear requires 2 yards of fabric, 5 hours of assembly, and 1 piece of trim. Profit contribution for each animal type is also provided as well as availability of each recource. yards of fabric hours of assembly pieces of trim Profit ear 2 1 $2 Rabbit 3 4 $5 Dog Total availability 3 1 2 $3 250 300 200 The decision variables for the problem are: x1 = number of bears x2 = number of rabbits x3 = number of dogs The appropriate linear programming model as well as the LINDO output are shown on the next page. Using the output answer the following questions: 1. How many of each animal should be produced? What level of profit will be attained? 2. Which resources are scarce (another way of asking which resources are valuable)? 3. If Williams could obtain fabric, time, or trim at zero cost, which resource would be most attractive? 4. If the minimum requirement constraint were eliminated, would there be any change in the production pattern? 5. The assemblers offer to work 50 additional hours at $4.75 an hour. What would Williams say to this? 6. What would happen if the profit on bears increased to $6? 7. What would happen if an actual count of the inventory revealed that there was really only 175 pieces of trim? 8. Would the company be willing to buy more fabric? How much, and at what price? 9. What would happen if a cutting error made 12 yards of fabric unusable? (1.e. there is a loss of 12 yards of fabric). 10. If the price on dogs is cut so that the profit drops to $2.25, will there be any changes for the company? MAX 2X1 + 5X2 + 3 X3 SUBJECT TO 2) X1 + X2 + X3 >= 100 3) 2X1 +2 X2 + 3 X3