Business, 30.03.2021 17:00 haileesprague1578

The LP problem whose output follows determines how many necklaces (X1), bracelets (X2), rings (X3), and earrings (X4) a jewelry store should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions. MAX
100X1+120X2+150X3+125X4
1) X1+2X2+2X3+2X4<108
2) 3X1+5X2+X4<120
3) X1+X3<25
4) X2+X3+X4>50 plus nonnegativity

Target Cell (Max)
Cell Name Final Value
$B$9 profit 7475

Adjustable Cells

Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$G$3 x1 (necklaces) 8 0 100 1.00E+30 12.5
$G$4 x2 (bracelets) 0 -5 120 5 1.00E+30
$G$5 x3 (rings) 17 0 150 12.5 25
$G$6 x4 (earrings) 33 0 125 25 5

Final Shadow Constraint Allowable Allowable
Cell Name Value Price R. H. Side Increase Decrease
$C$7 usage space 108 75 108 15.75 8
$D$7 usage setup time 57 0 120 1.00E+30 63
$E$7 usage marketing1 25 25 25 33 17
$F$7 usage marketing2 50 -25 50 4 8.5

Required:
a. What is the optimal solution and what profit will it return?
b. How much would you be willing to pay to reduce the setup time restriction by 20 minutes?
c. If the profit for 1 unit of necklace were to drop by $10 what impact will this have?
d. Do the same for earrings?

Answers: 3

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