1. The Stratton Company produces two basic types of plastic pipe. Three resources are crucial to the output of pipe: extrusion hours, packaging hours, and a special additive to the plastic raw material. The following data represent next week's situation. All data are expressed in units of 100 feet of pipe. Resource Extrusion Packaging Additive Type 4 br 2 hr 21b Product 1 Type 2 6 hr 2 br 1 lb $6 per unit Dark sold $5 per unit Light sold. Resource Availability 48 hr 18 hr 16 lb The contribution to profits and overhead per 100 feet of pipe is $34 for type 1 and $40 for type 2. Formulate a linear programming model to determine how much of each type of pipe should be produced to maximize contribution to profits and to overhead. Please submit your excel file with solver output. Please follow the Linear Programming material pages 10 to 13. 2. Consider a chocolate manufacturing company which produces only two types of chocolate - Dark and Light. Both the chocolates require Milk and Choco only. To manufacture each unit of Dark and Light, following quantities are required: Each unit of Dark requires 1 unit of Milk and 3 units of Choco Each unit of Light requires 1 unit of Milk and 2 units of Choco The company kitchen has a total of 5 units of Milk and 12 units of Choco. On each sale, the company makes a profit of Now, the company wishes to maximize its profit. Formulate a linear programming model to determine how many units of Dark and Light should it produce respectively. 3. The Attaran Corporation manufactures two electrical products: portable air conditioners and portable heaters. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each heater must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Product Air Cond. Heater Wiring (hours) 3 2 Drilling (hours) 2 1 Each air conditioner sold yields a profit of $25. Each heater assembled may be sold for a $15 profit. Please define the decision variables, the objective function, and formulate the constraints. Next, please formulate the LP model and solve for the optimal values of the decision variables and the maximum profit on Excel Solver.