Dunder Miflin Technologies (DMT) produces trendy tablets. Two of its models are the market leaders: Supercool and Ubercool. Supercool has a profit margin of $200 and Ubercool brings in a profit of $250. Producing Supercool requires 1 processor and 2 standard memory chips whereas Ubercool needs 2 processors and 3 premium memory chips. DMT has 150 processors, 120 standard memory chips and 150 premium memory chips. Variable definitions for the linear programming problem, the profit maximization problem and the sensitivity analysis are provided below. You are required to answer the questions which follow using this information.
Let, S = number of Supercool models produced
U = number of Ubercool models produced
Max. 200 S+ 250U
Subject to:
S + 2U < 150 (Processor Constraint)
2S < 120 (Standard Chip Constraint)
3U < 150 (Premium Chip Constraint)
S, U > 0
Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $A$2 Supercool 600 200 1 E+30 75
$B$2 Ubercool 450 250 150 XXX Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $A$9 Processor 150 XXX 150 10 $A$10 Standard Chip 120 37.5 120 180 $A$11 Premium Chip 135 XXX 150 1E+30
1. What is the shadow (dual) price of the constraint "Premium Chip"?
2. In the above sensitivity analysis, what is the allowable decrease for the "Ubercool" model objective coefficient?
3. What is the shadow (dual) price for the "Processor" constraint in the sensitivity analysis?
4. Suppose Sabre, a chip manufacturer, offers to sell 200 Standard Chips to DMT. At which of the following prices would DMT definitely be willing to purchase these 200 Standard Chips?
I. $6,000
II. $6,500
III. $7,000
5. Suppose that due to a delay at their premium chip supplier, Dunder Miflin obtains 20 fewer premium chips than expected. How will this, if any, affect the optimal solution and the profit?
6. If the objective function coefficient of "Supercool" is reduced by more than $100, which of the following could be the new optimal solution for "Ubercool"?