0.80 0.30 0.40 50 0.50 0.16 0.30 0.60 The optimal solution is x1=1, x2=0, X3=1 3. A toy manufacturer has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $50,000 for toy 1 and $80,000 for toy 2. Once these costs are covered, the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2 9L The company has two factories that are capable of producing these toys. However, to oid doubling the start-up costs, just one factory would be used and the choice would be based on maximizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced Toy 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2 toy 2 can be produced at the rate of 40 per hour in factory 1 and 25 per hour in factory 2 factories 1 and 2, respectively, have 500 and 700 hours of production time available before Christmas that could be used to produce these toys It is not known whether these two toys would be continued after Christmas Therefore, the problem is to determine how many units (if any) of each new toy should be produced before Christmas in order to maximize the total profit Formulate an IP model for this problem. (10 points) Solution: we set produce the two toys x1, x22 The optimal solution is x1=1, x2=0, x3=1 3. A toy manufacturer has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $50,000 for toy 1 and $80,000 for toy 2. Once these costs are covered, the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2. The company has two factories that are capable of producing these toys. However, to avoid doubling the start-up costs, just one factory would be used and the choice would be based on maximizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced. Toy 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2. toy 2 can be produced at the rate of 40 per hour in factory 1 and 25 per hour in factory 2. factories 1 and 2, respectively, have 500 and 700 hours of production time available before Christmas that could be used to produce these toys. It is not known whether these two toys would be continued after Christmas. Therefore, the problem is to determine how many units (if any) of each new toy should be produced before Christmas in order to maximize the total profit. Formulate an IP model for this problem. (10 points) Solution: we set produce the two toys x1,x2 2 0.15 0.20 0.40 0.06 0 1 2 0 1 2 0 0.48 0.30 0.16 0.80 0.50 0.30 0.60 0.40 0.60 0.20 0.60 0.40 0.30 0.50 0.80