Question

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	60	0	200	1E+30	75
$B$2	Ubercool	45	0	250	150	XXX
		Final	Shadow	Constraint	Allowable	Allowable
Cell	Name	Value	Price	R.H. Side	Increase	Decrease
$A$9	Processor	150	XXX	150	10	90
$A$10	Standard Chip	120	37.5	120	180	20
$A$11	Premium Chip	135	XXX	150	1E+30	15

14. 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”?

Group of answer choices

45, 50 and 55 are all possible.

Both 50 and 55 are possible.

45

50

55

Answer 1

Allowable decrease for objective function of super cool is $75. As current reduction is greater than the allowable decrease , the current optimal solution will not remain the same. Current value of Uber cool is 45. It will not be 45 anymore, It will take value higher than 45.

Therefore, new optimal solution for Uber cool could be

Both 50 and 55 are possible.