Exhibit D. The ABC Company manufactures three products X, Y, and Z. Two critical resources have limited availability: 2400 labor hours and 2000 pounds of material available for the coming week. Product X requires 1 hour of labor and 1.5 pounds of material per unit; Product Y requires 0.5 hour of labor and 1.5 pounds of material per unit; Product Z requires 2 hour of labor and 1.5 pounds of material per unit. The gross profit margin is $12, $10, and $18 for each of X, Y, and Z before considering the following two factors. First, if a product is produced in a week, a weekly setup cost for the machinery will incur. For product A, the machinery setup cost is $800; product B machinery costs $1000, and product C machinery costs $2000 to set up. There is no machinery setup cost if a product is not produced in a week. Second, products Y and Z have additional marketing cost as a function of units produced in order to sell them: 0.15 Y2 for product Y and 0.2 Y2 for product Z. Help the company find the best production plan for the coming week that will maximize the total net profit. D-1. (1) What kind of problem is it? What analytic tool can be used to solve the problem? Explain why. (2) Formulate the problem to find the optimal production plan for the coming week. How many units of each product should be produced? What is the maximum total profit? Is there any resource that is not used? If so, how many units? Exhibit D. The ABC Company manufactures three products X, Y, and Z. Two critical resources have limited availability: 2400 labor hours and 2000 pounds of material available for the coming week. Product X requires 1 hour of labor and 1.5 pounds of material per unit; Product Y requires 0.5 hour of labor and 1.5 pounds of material per unit; Product Z requires 2 hour of labor and 1.5 pounds of material per unit. The gross profit margin is $12, $10, and $18 for each of X, Y, and Z before considering the following two factors. First, if a product is produced in a week, a weekly setup cost for the machinery will incur. For product A, the machinery setup cost is $800; product B machinery costs $1000, and product C machinery costs $2000 to set up. There is no machinery setup cost if a product is not produced in a week. Second, products Y and Z have additional marketing cost as a function of units produced in order to sell them: 0.15 Y2 for product Y and 0.2 Y2 for product Z. Help the company find the best production plan for the coming week that will maximize the total net profit. D-1. (1) What kind of problem is it? What analytic tool can be used to solve the problem? Explain why. (2) Formulate the problem to find the optimal production plan for the coming week. How many units of each product should be produced? What is the maximum total profit? Is there any resource that is not used? If so, how many units
