Below given is the linear programming model at a manufacturingfirm which produces and sells
for different bags: small bags, medium bags, standard bags,and deluxe bags.
DECISION VARIABLES:
xi- Number of bags for group i to produce, i=1(small bag),2(medium bag), 3(standard bag),
4(deluxe bag).
OBJECTIVE FUNCTION:
Maximize profit, z = 6.5x1 + 7.5x 2 +10x3 + 9x4
CONSTRAINTS:
0.55x1 + 0.6x 2 + 0.7x3 + x4 ? 630 (Cutting and dyeing)
0.425x1 + 0.45x 2 + 0.5x3 + 0.833 x4 ? 600 (Sewing)
0.55x1 + 0.6x 2 + x3 + 0.67x4 ? 708 (Finishing)
0.78x1 + 0.8x 2 + 0.1 x3 + 0.25x4 ? 135 (Inspection andPacking)
x1 , x 2 , x3, x4 ? 0
The Excel sensitivity report for this linear model is providedbelow:
Microsoft Excel 12.0 Sensitivity Report
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$26 # Small bag 0.000 ?0.470 6.5 0.470 1E+30
$C$26 # Medium bag 79.508 0 7.5 7.918 0.480
$D$26 # Standard bag 640.789 0 10 2.479 8.702
$E$26 # Deluxe bag 29.259 0 9 77.667 1.962
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$B$32 Cutting and dyeing 525.516 0 630 1E+30 104.484
$B$33 Sewing 600 0.246 600 1702.313 232.986
$B$34 Finishing 708 9.679 708 161.682 576.099
$B$3 Inspection &Packaging 135 1.977 135 452.69958.563
Answer the following questions using the above sensitivityreport:
NOTE:
1. EACH QUESTION THAT FOLLOWS REFERS TO THE ORIGINAL PROBLEM.THAT IS, EACH QUESTION IS INDEPENDENT OF THE OTHER QUESTIONS.
2. IF IT IS IMPOSSIBLE TO ANSWER THE QUESTION WITHOUTRESOLVING THE
PROBLEM, YOU MUST STATE THAT IN YOUR ANSWER AND BRIEFLYEXPLAIN
WHY. NO MARKS WILL BE GIVEN FOR UNSUPPORTED ANSWERS. SHOW ALLYOUR CALCULATIONS CLEARLY.
a. Identify the optimal solution and its objective functionvalue?
b. Find the hours used for each process (cutting and sewing,finishing, inspection and
packing):
c. If the profit from small bag increases to $7.25, what willbe the new optimal solution and
new objective function value?
d. If the profit from the standard bag increases to $12.00,what will be the new optimal
solution and new objective function value?
e. Due to the expected maintenance work in the cutting anddyeing department, the hours
available in cutting and dyeing will decrease to 550 hours.What is the new optimal
solution and new objective function value?
f. The firm can get 50 more hours in cutting dyeingdepartment, find its new optimal
solution and new objective function value.
g. The firm can produce another bag called “School bags” at aprofit of $5.5. One school
required 0.5 hours for cutting and dyeing, 0.42 hours forfinishing, and 0.35 hours for
inspection and packing. Find the new optimal solution and newobjective function value.
h. The firm wants to produce small bags at least as the numberof medium bags. What will
be the new optimal solution and new objective function value?
i. If the profit from deluxe bag is increased to $15 and thehours available in the inspection
and packing is increased to 200 hours, find the new optimalsolution and the new
objective function value.
j. If the available hours for finishing is decreased to 500hours, find the new optimal
solution and the new objective function value.
