Question: 3. Consider the product mix problem summarized in the table with 3 products (A, B and C) and 5 types of resources (1,2,3,4,5). There may

3. Consider the product mix problem summarized in

3. Consider the product mix problem summarized in the table with 3 products (A, B and C) and 5 types of resources (1,2,3,4,5). There may be multiple workers working in parallel for each resource. Assume that all workers have 8 hours per day. Demand is assumed to be 70 units/day for Product A, 50 units/day for Product B and 40 units/day for Product C. The number of workers in each resource and the times required for each activity (product) in each resource is given in the following table. Resources # of workers 1 2 2 1 3 2 4 1 5 3 Activity time for A (Min/Unit) 5 3 15 0 Activity time for B (Min/Unit) 5 4 0 4 10 Activity time for C (Min/Unit) 5 5 0 3 10 10 a. c. What is the maximum flow rate if demand must be served in the mix determined by the demand rate (7 units of A, 5 units of B and 4 units of C)? b. What is the bottleneck for the maximum flow rate? What are the utilizations of resources? Can the given daily demands be satisfied? d. Now assume that workers can be assigned to multiple resources. Keeping current workforce, formulate and solve a linear program to find the optimal workforce assignment to maximize the flow rate? Note: You can assume that fractional assignments can take place. To model this let wibe the amount of workforce assigned to each resource and wi = 9. What are the utilizations of resources? f. Now assume that demand is 35 units/day for Product A, 25 units/day for Product B and 20 units/day for Product C. What are the utilizations of resources? Note: The system is now demand constrained and we must have Xa

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