Reference no: EM132240075

Joe Bagov makes 500 donuts in Wayne and has customers in Tilden who want 100 donuts, in Norfolk who want 200 donuts and in South Sioux City who want 200 donuts. Joe has distributors in Wisner and Laurel who will get the donuts and take them to the final destinations. Joe has to decide how much each distributor will take to each location. The locations have the following numbers to identify the locations: Wayne 1, Laurel 2, Wisner 3, Tilden 4, Norfolk 5, and South Sioux City 6. It costs 10 cents per donut to get donuts from Wayne to the distributors in both Laurel and Wisner. The costs per donut to go from Laurel to Tilden, Norfolk and South Sioux City are 15, 10, and 15 cents, respectively. Similarly, from Wisner to these locations, respectively, are 13, 9 and 16 cents. 1. How many variables are there in a linear programming problem to minimize cost of getting donuts from Wayne to Tilden, Norfolk and South Sioux City in this transshipment problem? 2. How many constraints are there in a linear programming problem to minimize cost of getting donuts from Wayne to Tilden, Norfolk and South Sioux City in this transshipment problem(excluding the non-negativity constraints)? 3. How many donuts are shipped on each route and what is the minimum cost of the shipping? 4. Would the shipping amounts change if the cost of shipping from Wayne to Laurel changed to 6 cents? Yes or no? Why (why in the sense of what you see on an Excel printout of the problem, not why in terms of adjustments on routes)? 5. What does the reduced cost on the variable x36 mean (use the number for the reduced cost as part of your answer)? 6. What would happen to the total cost of shipping if Tilden only wanted 99 donuts?