Linear programming - sensitivity analysis - using Solver. Below we solve this LP with the Solver add-in that comes with Microsoft Excel. If you click here. Constraints which are not tight are called loose or not binding.

Linear programming - sensitivity analysis - using Solver OR-Notes OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following. A full list of the topics available in OR-Notes can be found. Linear programming - sensitivity analysis - using Solver Recall the production planning problem concerned with four variants of the same product which we formulated as an LP. To remind you of it we repeat below the problem and our formulation of it. Production planning problem A company manufactures four variants of the same product and in the final part of the manufacturing process there are assembly, polishing and packing operations.

For each variant the time required for these operations is shown below (in minutes) as is the profit per unit sold. Assembly Polish Pack Profit (£) Variant 1 2 3 2 1.50 2 4 2 3 2.50 3 3 3 2 3.00 4 7 4 5 4.50 • Given the current state of the labour force the company estimate that, each year, they have 100000 minutes of assembly time, 50000 minutes of polishing time and 60000 minutes of packing time available. How many of each variant should the company make per year and what is the associated profit?

• Suppose now that the company is free to decide how much time to devote to each of the three operations (assembly, polishing and packing) within the total allowable time of 210000 (= 100000 + 50000 + 60000) minutes. How many of each variant should the company make per year and what is the associated profit?

Below you can find the optimal solution and the sensitivity report. It is optimal to order 94 bicycles and 54 mopeds. This solution gives the maximum profit of 25600. This solution uses all the resources available (93000 units of capital and 101 units of storage).

You can find these numbers in the Final Value column. Reduced Cost The reduced costs tell us how much the objective coefficients (unit profits) can be increased or decreased before the optimal solution changes. If we increase the unit profit of Child Seats with 20 or more units, the optimal solution changes.

At a unit profit of 69, it's still optimal to order 94 bicycles and 54 mopeds. Below you can find the optimal solution. Move media player for mac. At a unit profit of 71, the optimal solution changes. Conclusion: it is only profitable to order child seats if you can sell them for at least 70 units. Shadow Price The shadow prices tell us how much the optimal solution can be increased or decreased if we change the right hand side values (resources available) with one unit. With 101 units of storage available, the total profit is 25600.

Below you can find the optimal solution. With 102 units of storage available, the total profit is 25700 (+100). Note: with a shadow price of 100 for this resource, this is according to our expectations. This shadow price is only valid between 101 - 23,5 and 101 + 54 (see sensitivity report).