a) [8 points] 1 . What is the minimum cost attainable under an optimal plan? The minimum cost attainable is $ ........ (round to nearest dollar). 1i. How many products of each type should be produced in-house, obtained from small- supplier, and obtained from large-supplier under this optimal plan? Number of jobs of processed under optimal solution (round to nearest integer): Number of products A B C D In-house production Obtained from small-supplier Obtained from large-supplier 111. How many units of RM1, RM2, and RM3 are used up under this optimal plan? Resources used under optimal solution: Resource Units used Available RM1 1,200,000 RM2 2,500,000 RM3 2,880,000 b) The company has located an alternate supplier (New-Supplier) for product D who can supply at most 10,000 units of product D in the upcoming month. The price per unit of D is subject to negotiations. What is the maximum amount that the company should be willing to pay New-Supplier per unit of product D? Justify your answer by explaining your approach. [4 points]Question 3. Optimization Models [12 Points] A company provides 4 types of products to a client - A, B, C, and D. In-house production costs are estimated to be $2, $3, $4, and $5 per unit for products A, B, C, and D respectively. Each product requires three types of raw materials - RM1, RM2, and RM3 - for in-house production: 2 units of RM1, 2 units of RM2, and 2 units of RM3 per unit of product A; . . 2 units of RM1, 3 units of RM2, and 3 units of RM3 per unit of product B; 1 unit of RM1, 4 unit of RM2, and 5 units of RM3 per unit of product C; and 2 units of RM1, 4 units of RM2, and 5 units of RM3 per unit of product D. Over the upcoming month the company has 1,200,000 units of RM1, 2,500,000 units of RM2, and 2,880,000 units of RM3 available. Because of contractual obligations the company must provide the client with 500,000 units of product A, 400,000 units of product B. 300,000 units of product C, and 100,000 units of product D in the upcoming month. Limited resource availability prevents the company from meeting the entire demand for all products through in-house production alone. The company has two other options: it can obtain products from either a small-supplier or a large-supplier; no resources are used for products obtained from suppliers. The small-supplier can supply at most 10,000 units of each product; there is no limit to the quantities of products that the large-supplier can supply. The small-supplier charges $3, $4. $5, and $6 per unit of products A, B. C, and D. respectively. The large-supplier charges $4, $5, $6, and $8 per unit of products A, B, C, and D, respectively For your convenience, the information presented above is summarized in the table below: Product A B C D Available Production RM1 2 2 2 1,200,000 requirement RM2 2 3 4 2,500,000 RM3 2 5 2,880,000 Demand 500,000 400,000 300,000 100,000 Capacity of small supplier 10,000 10,000 10,000 10,000 for production $2 $3 $4 $5 Cost per unit from small supplier $3 $4 $5 $6 from large supplier $4 $5 $6 $8 The company has to meet its contractual obligations in the upcoming month at minimum cost. Formulate the problem as a linear program (LP), solve the LP, and perform sensitivity analysis to answer the questions that follow
