1. (25 points) A Chemical company manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $400 and yields 300 units of A, 100 units of B, and 100 units of C. Running process 2 for an hour costs $100 and yields 100 units of A and 100 units of B. To meet customer demands, at least 1000 units of A, 300 units of B, and 300 units of C must be produced daily. Determine a daily production plan that minimizes the cost of meeting the company's daily demands. 2. (25 points) A furniture company manufactures desks and chairs. Each desk uses four units of wood, and each chair uses three units of wood. A desk contributes $400 to profit and chair contributes $250. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. There are 2000 units of wood available. What is the maximum company's profit? 3. (25 points) Maggie Stewart loves desserts, but due to weight and cholesterol concerns she has decided she must plan her desserts carefully. There are two possible desserts she is considering: snack bars and ice cream. After reading the nutrition labels on the snack bar and ice cream packages, she learns that each serving of snack bar weighs 37 grams and contains 120 calories and 5 grams of fat. Each serving of ice cream weighs 65 grams and contains 160 calories and 10 grams of fat. Maggie will allow herself no more than 3150 calories and 175 grams of fat per week in her desserts, but because she loves dessert so much, she requires at least 840 grams of desserts per week. Each serving of ice cream has 3.5 grams of proteins and each serving of snack bar has 2.5 grams of proteins. Find the weekly dessert plan that stay within her constraints and maximizes total protein of her dessert (write down the mathematical model and solve the problem using graphical approach)? Round the answer to nearest integer. 4. (25 points) Yorktown Inc, makes two different types of cricket bats. One bat for aggressive batting style and one bat for defensive batting style. The company has 900 hours of production time available in its wood cutting department, 300 hours available for finishing department, and 90 hours available in its packaging and shipping department. The production time requirements and the profit contribution per bat are given in the following table. Wood Production Time (hours) Packaging Cutting Finishing and Shipping Profit/Bat Model Aggressive 2 1/3 1/5 $6 Defensive 1.2 1/2 1/9 $7 1. What is the linear programming model for this problem? 2. Find the optimal solution using the graphical solution procedure. How many bats of each model should Yorktown manufacture? 3. How many hours of production time will be scheduled in each department? 4. What is the slack time in each department?