# LP Analysis: Product Mix Problem

Topics: Profit Pages: 2 (521 words) Published: February 3, 2012
LP Analysis - Product Mix Problem: 2 products, 2 constraints

1. Max OF = \$15,263.16
2.Optimal Soln: X1 = 2894.74 X2 = 263.16
3.X1 is more than 10 times X2
4.Profit: X1 = \$5.00 & X2 = \$3.00, profit margin of IPODs is 166% larger than DVD’s not 10 times. 5.Conventional approach: product mix is dependent on profit margins.

1. LHS = RHS for both constraints, no leftover resources.
2.Limitation on resources constrains expansion of product mix and greater profitability. 3.These are referred to as Binding constraints, i.e. no leftover resources 4.SLACK – leftover or unused resource (or capacity) for M.P. net profit = SP – MP

In general (without market info): since SP testing > SP assembly, use available funds to hire testers since they are much more (3 times) profitable.

Principle:
If Slack or Surplus = 0, Then the SP > 0. No leftover resource exist so additional resources can be converted into products which will generate additional profits, sp >0. If Slack or Surplus > 0, Then SP = 0. Since there are idle resources (leftovers), additional resources will also be idle, no new products and profit remains unchained, sp =0.

Question 2: How much additional resources should be acquired?

Acquire additional resources as long as SP remains unchanged, or as long as Slack = 0 Use LP to determine range. This is referred to as Right Hand Side Ranging – RHS ranging.

RHS ranging Definition: Range over which RHS changes while the SP does not change.

More resources lead to increased production, but mix is still determined by profitability

Revelation #1
Notice as resource availability changes, product mix changes in ways contradictory to when profit margins are used to determine product mix.

Question 4: conventional wisdom
1.Product mix changes as profit margins of products change. 2.Production levels of a product change proportionally to profit...