The LP Problem formulation is given below which determines how many necklaces (X_{1}), bracelets (X_{2}), rings (X_{3}) and ear rings (X_{4}), a jewellery 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 1 and 2 respectively.

Max | 100 X_{1} |
+ 120 X_{2} |
+ 150 X_{3} |
+ 125 X_{4} |
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Subject to: | |||||||

X_{1} |
+ 2 X_{2} |
+ 2X_{3} |
+ 2X_{4} |
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3X_{1} |
+ 5 X_{2} |
+ X_{4} |
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X_{1} |
+ X_{3} |
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X_{2} |
+ X_{3} |
125 X_{4} |
>=108 |

Solve the problem in Excel and answer the following questions.

(First 10 are of 1 mark each and last 5 are of 2 Marks each)

A. What is the Number of necklaces to be stocked?

B. What should be the value of bracelet coefficient so that it appears in optimal solution?

C. What is the Number of rings to be stocked?

D. Which constraints are binding?

E. What is the value of optimal value of Profit?

F. What is theRange of optimality of necklaces?

G. How much space will be left unused?

H. How much time will be used?

I. What is theRange of optimality of ear rings?

J. What is theRange of Feasibility Display space?

K. What would the Profit be if theDisplay space is increased by 5 units?

L. What would the Profit be if thetime to set up the display is decreased by 10 units?

M. You are offered the chance to obtain more space. The offer is for 15 units and the total price is 1500. What should you do? Answer in yes or no

N. Which resource should the company work to increase, Space or Time.

O. Over what range of marketing restriction 1 is the dual price applicable?