Shadow Prices Revisited Jason's House of Cheese offers two cheese assortments for holiday gift giving. In his supply ref

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Shadow Prices Revisited Jason S House Of Cheese Offers Two Cheese Assortments For Holiday Gift Giving In His Supply Ref 1 (358.12 KiB) Viewed 27 times

This is the entire problem. I only need to solve point 6. Here,
you can find below the dual problem.

Shadow Prices Revisited Jason S House Of Cheese Offers Two Cheese Assortments For Holiday Gift Giving In His Supply Ref 2 (15.17 KiB) Viewed 27 times

The economic interpretation should look as below.

Shadow Prices Revisited Jason S House Of Cheese Offers Two Cheese Assortments For Holiday Gift Giving In His Supply Ref 3 (266.38 KiB) Viewed 27 times

Shadow Prices Revisited Jason's House of Cheese offers two cheese assortments for holiday gift giving. In his supply refrigerator, Jason has 3600 ounces of cheddar, 1498 ounces of Brie, and 2396 ounces of Stilton. The St. Nick assortment contains 10 ounces of cheddar, 5 ounces of Brie, and 6 ounces of Stilton. The Holly assortment contains 8 ounces of cheddar, 3 ounces of Brie, and 8 ounces of Stilton. Each St. Nick assortment sells for $16, and each Holly assortment sells for $14. How many of each assortment should be produced and sold in order to maximize Jason's revenue? 1. Solve the problem geometrically. 2. By looking at your graph from part 1, can you determine the shadow price of cheddar? 3. Solve the problem by the simplex method. The solution should be the same as in part 1. Verify your answer to part 2 by looking at your final tableau. 4. What are the shadow prices for Brie and Stilton? 5. What would the maximum revenue be if there were 3620 ounces of cheddar, 1500 ounces of Brie, and 2400 ounces of Stilton? 6. Go back to the original problem, and state its dual problem. What information do the original slack variables u, v, and w give us about the dual problem? Determine the solution to the dual problem from your final tableau in part 3, and give an eco- nomic interpretation.

Minimize the objective function: M= 3600u + 1498 +2396w subject to the contraints: 10u + 5v +6w > 16; 8u + 3v +8w > 14; u> 0; v>0; w >0;

When we gave an economic interpretation to the dual of the furniture manufactur- ing problem, we first had to assign units to each of the variables of the dual problem. For instance, u was in units of profit per labor-hour of carpentry, or profit labor-hours of carpentry The systematic procedure that follows can often be used to obtain the units for the vari- ables of the dual problem from units appearing in the primal problem. Assume that the primal problem is stated in one of the two forms given previously. 1. Replace each entry of the matrix A by its units, written in fraction form. Label each column and row with the corresponding variable. 2. Replace each entry of the matrix C by its units, written in fraction form. 3. To find the units for a variable of the dual problem, select any entry in its row in A, divide the corresponding entry in C by the entry chosen in A, and simplify the fraction. For the furniture manufacturing problem, the matrices are у labor-hours of carpentry labor-hours of carpentry u chair sofa labor-hours of finishing labor-hours of finishing = A chair sofa labor-hours of upholstery labor-hours of upholstery w chair sofa profit profit chair sofa ע ]-c . =

Using the first entry in the row labeled u, we find that the units for u in the dual problem are profit labor-hours of carpentry_profit chair chair chair chair labor-hours of carpentry profit labor-hours of carpentry Here, u is measured in dollars per labor-hour of carpentry.