A manufacturer of tires produces two kinds of tires. The premium tire, The Last -Forever, is a steel -belted, puncture -resistant, long -wear tire that holds all records for quality

4-46. A manufacturer of tires produces two kinds of tires. The premium tire, The Last -Forever, is a
steel -belted, puncture -resistant, long -wear tire that holds all records for quality within the industry.
The other tire, Lane -Handler, is a simple low cost 40,000 mile warranty unbranded tire. The
Last -Forever contributes $50 per tire to the bottom line for the company, while the Lane -Handler
contributes only $10 to the bottom line. Both tires are manufactured at the same factory and require
the same machines to be produced. Malchine A and machine B are both used in the two-step process
used to make the tires. The time consumed in hours on each machine to fabricate a tire are given
below.
Total Hours
Lane -Handler Last -Forever Available
Machine A 1 4 120
Machine B 2 2 100
Twenty Lane -Handlers have been promised to a valued dealer and 4 Last-Forevers have been
promised the owner's son.
(a) Find the product mix that maximizes profit.
(b) What is the OV?
(c) If machine B hours could be increased to 120, then what would be the change in the OV?
(d) What would be the impact if a maintenance problem reduced available machine A hours
to 100?

4-49. Karma Computers produces two computer models, Standard and Deluxe. A Standard model is
produced by assembling a single disk drive with a Standard Chassis. A Deluxe model is produced
by assembling two disk drives with a Deluxe Chassis. The Standard model has a net profit per unite
$300 while the Deluxe model has a net profit per unit of $400. The current inventory of Karma
consists of 60 Standard Chassis, 50 Deluxe Chassis and 120 Disk Drives.
(a) Formulate the Karma LP model.
(b) Optimize the Karma model and use that result to fill in the missing values in the blank
cells of the worksheet in Figure 4.22.
1 KARMA COMPUTER
2 Decision Variables S
3 Quantity I PROF 11
4_Contrib. Margin $300 $400
Subject To: LI IS RHS Slack
-5 6H Schas Constr 1 < 60
Dchas Constr 1 < 50
Ddrive Constr


Chapter 4 Linear Optimization: Sensitivity Analysis
(c) Use the results from the worksheet above to fill in the missing values for Final Value and
Constraint R.H. Side in the blank cells of the Karma model Sensitivity Report below.
Next, determine the values of the remaining missing cells in the Sensitivity Report in
Figure 4.23.
Microsoft Excel 15.0 Sensitivity Report
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$3 Quantity S 300
$C$3 Quantity D 400 200 400
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$D$6 Schas Constr LHS 60 60
$D$7 Dchas Constr LHS 50 20
$D$8 Ddrive Constr LHS 60