Yonsei is preparing to launch two new products, product A and product B. Each product has three components: a base, a body and a top. The same base is used for both products, but the bodies and the tops are different. All components can be manufactured by Yonsei or purchased from outside suppliers. The manufacturing costs and purchase prices for the components ate summarized in the following table. Base Body for product A Body for product B Top for product A Top for product B Unit Manufacturing Cost $0.50 $3.75 $3.30 $0.60 $0.75 Unit Purchasing Price $0.60 $4.00 $3.90 $0.65 $0.78 Yonsei forecasts that 3000 product A and 2000 product B will be needed and Yonsei has to satisfy this demand. However, manufacturing capacity is limited. Yonsei can use at maximum 200 hours of manufacturing time, and the following table shows the manufacturing time (in minutes) per unit required for all components. Base Body for product A Body for product B Top for product A Top for product B Unit Manufacturing time 1.1 3.0 2.2 1.0 1.4 1. (20 points) Construct an LP model for this problem. Identify decision variables, constraints, and an objective function. 2. (10 points) Formulate a spreadsheet model. 3. (10 points) Yonsei decided to use at maximum 50 hours of overtime in order to produce more products. Overtime involves a premium at the additional cost of $7 per hour. Yonsei wants to minimize the total cost. By considering the hours of overtime that will be used, reformulate an LP model (rewrite the algebraic model). Yonsei is preparing to launch two new products, product A and product B. Each product has three components: a base, a body and a top. The same base is used for both products, but the bodies and the tops are different. All components can be manufactured by Yonsei or purchased from outside suppliers. The manufacturing costs and purchase prices for the components ate summarized in the following table. Base Body for product A Body for product B Top for product A Top for product B Unit Manufacturing Cost $0.50 $3.75 $3.30 $0.60 $0.75 Unit Purchasing Price $0.60 $4.00 $3.90 $0.65 $0.78 Yonsei forecasts that 3000 product A and 2000 product B will be needed and Yonsei has to satisfy this demand. However, manufacturing capacity is limited. Yonsei can use at maximum 200 hours of manufacturing time, and the following table shows the manufacturing time (in minutes) per unit required for all components. Base Body for product A Body for product B Top for product A Top for product B Unit Manufacturing time 1.1 3.0 2.2 1.0 1.4 1. (20 points) Construct an LP model for this problem. Identify decision variables, constraints, and an objective function. 2. (10 points) Formulate a spreadsheet model. 3. (10 points) Yonsei decided to use at maximum 50 hours of overtime in order to produce more products. Overtime involves a premium at the additional cost of $7 per hour. Yonsei wants to minimize the total cost. By considering the hours of overtime that will be used, reformulate an LP model (rewrite the algebraic model)