Car Manufacturing Industry: A Case Study A car manufacturing company needs to find the proper combination of four materials, such that all four metals are present in the alloy, in proper proportion as per the standards prescribed by ARAI. Consider the table given below that gives the chart of the materials, metals, and ARAI-prescribed standards: Weight of metal in g per 100 g of the material | ICMR Material #1 #2 #3 #4 Stds. in g Metal 1 12 4 6 6 Metal 2 2 8 2 6 At most 50 | At most 30 Let xi Metal 3 4 2 6 4 At most 36 Metal 4 2 4 4 4 At least 24 Cost per 100 g in Rs. 20 40 20 20 denote the number of slabs of material i of 100g each. Note that slabs can be further dividied. Please take note of the following: According to the ARAI standards, the weight of metals 1, 2, and 3 should be at most 50, 30, and 36 g, respectively, and the weight of metal 4 should be at least 24 g in the alloy. Respond to Questions 4 and 5 based on Phase 2 case. Question 4 Formulate an LPP using the above details to minimize the total cost of materials. Question 5 Using the M method, solve the LPP formulated in Question 4 and find all the optimal solutions (if they exist).