productionoperation management Fall 2013 1 Test Simplex Meth

Fall 2013 -#1 Test Simplex Method of Linear Programming-Problem to Solve Hidden Valley Orchard sells apples to wholesalers. Standard Lc) containers. A small container of apples yields a profit of $20, a medium container, $40, and a large container, $60. Each shipment s prepared manually, requiring apples, picking/cleaning/packing time, and packing materials shipments can be packed in small (SC), medum (MC), or large Small containers of apples require 12 apples, 5 minutes of picking/cleaning/packing time, and 1 pound of packing materias Medium containers require 36 apples, 10 minutes, and 2 pounds of the respective resources, while large cortainers eu 15 minutes, and 3 pounds of these same resources. In total, there are 120,000 apples, 15,000 minutes, and 3,800 pounds of the resources available. Using the above information, set up this problem by set up this problem by completing the inital tableau below (iling in the blank cells) $20 $80 In Solution SC or X1 MC or X2 LC or X3 Production 120,000 s 0 s 0 s 0 3,600 1Zoo 20 40 60 For al cells in this tableau, do the calculations necessary to move from the first to the second tableau, complete the etation of the second tableau second tableau below eyl in te blank cells. and oner a fun nte $20 $40 $60 S2 In Solution S1 LC or X3 48,000 180/15 12 600 560 s o 40 60 Give a full interpretation of this second tableas 1. What resources are in solution? 2. How much profit has been made? 3. Which decision variable should be brought into solution and why? Non: tableauu hoy already reachad eptimal solutiou Which slack variable willeave solution and why? 5. What is the pivot element for this second tableau (please circle above)?

Solution

4.

SC or X1 because it has the greater negative value

5.

S3