A granola raw material manufacturer produces three different products. The customers specify restrictions of the final mix and the company mixes these products based on their objective (not relevant for the problem). A customer has the following requirements. Requirement 1: Product 1 must be exactly 20% of the final mix. Requirement 2: Product 2 must be at most 30% of the final mix. Requirement 3: Product 3 must be at least 40% of the final mix The company incorporates all these requirements into an optimization model after linearizing each constraint. The screenshot of the spreadsheet below represents the optimization model for the company.
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A manufacturer has three different types of raw materials A, B, and C in stock to manufacture three types of products 1, 2, and 3. There are two types of raw materials for each type of product. Table 1 shows the cost and on-hand supply of each type of raw materials, the number of each type of products needed, and a score (0 to 10) of the appropriateness match of each type of raw materials for making each type of products. The company would like to minimize the total cost while maximizing the total match score. Please formulate a mathematical model and use preemptive goal programming to compute a solution using GAMS to the model using target levels of $29,550 for cost and 13,000 for match and taking objectives in this order. Table 1. Supply, demand, and product match. Raw Material | Product Match Score (1, 2, 3) | Unit Cost ($) | On Hand (units) A | 7, 8, --- | 15 | 500 B | 10, ---, 6 | 25 | 630 C | ---, 10, 10 | 30 | 710 Demand (units) | 440, 520, 380 | | "---" indicates the raw material cannot be used to produce the product.
Sri K.
Dominador T.
3. (30 points) You make vanilla and blueberry yogurts with fresh milk. Every day you can purchase at most 150L of fresh milk. To make 1L of vanilla yogurt, you need exactly 0.75L of fresh milk. To make 1L of blueberry yogurt, you need exactly 0.5L of fresh milk. Vanilla yogurt sells for $150/L, and blueberry yogurt sells for $180/L. You have committed to selling 30L of vanilla yogurt and 15L of blueberry yogurt to CityU. Your yogurt is popular in the market and current demand far exceeds your production capacity. Any yogurt produced beyond the above requirements can be sold at your own yogurt store. You want to maximize your revenue. You construct a LP and use Solver to find the optimal solution. a. (10 points) Write down the linear program to determine the optimal production plan b. (15 points) Suppose you set up the LP model in Excel and here is the result of the sensitivity report: i. What will the production plan and revenue become if the revenue of vanilla yogurt is $160/L, instead of $150/L? ii. Do you detect the existence of multiple optimal solutions? iii. Suppose you find a new fresh milk supplier who can provide an additional 100L of fresh milk every day. How will this change the optimal revenue? c. (5 points) Suppose you want to make the blueberry flavor as a limited edition product. You decide that at most 20% of all yogurt sold in total are in blueberry flavor. Write a constraint to reflect this restriction on your production mix.
Akash M.
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