Parket Sisters Case 4(SHANIF)

Parket Sisters Case 4.2 a) Weekly product mix should consist of:

i.

Ball point

ii.

Mechanical Pencil

iii.

Fountain pen Weekly Net Profit

= 700 * 3 + 0 * 3 + 133.33 * 5 = 2766.65

b) It is non-degenerate because by looking at the zeros in allowable increase or decrease

tells us about its non-degeneracy. c) Yes the answer is Unique and there is only one optimal solution for that question. d) Marginal value of one more unit of chrome and plastic is: i.

Chrome = 0

ii.

Plastic = 1.1667

e) Yes, Company should buy because the shadow price of steel is $0.8 and local

company offering for $0.6 which is less. We will also look at the Allowable increase which is 555 so 500 is within the range. f) Product mix cannot be determined by sensitivity Analysis but profit can be

determined. Optimal Profit will be

= 500 * 3 + 133.33 * 5 = 2166.65

g) Shadow price of plastic is 1.167 and allowable increase is 200 so the net gain is

1.167 * 200 = 234 and the cost will be 1 * 500 = 500. So we should not buy. h) Yes the company should buy two lots of 100 ounces.

Net gain

= 1.167 * 200 = 234

Cost

=1 * 2(100) = 200

So The Optimal profit would be 3 * 1000 + 0 + 0 = $ 3000. i) Shadow price is 6.5 – 5.0 = 1.5 * 300 = 450 gain

1.17 * 300 = 351 loss 1000 will be reduced by 300 so LHS will be reduced by 351. j) Yes we should allow the decrease as there will be no effect on profit

1200 - 1000 =200 * 0 (shadow price) = 0. k) Yes the company should approve the new design as:

Cost = 1.1 * 1.2 + 2 * 0 + 2 * 0.8 = 2.88 And the selling price is 3. l) Current profit = 3

Allowable Decrease is = 0.78 the decrease is $ 2.5, which is within the range hence the optimal solution will remain same. m) 1.8*1.17 + .5*0 + 1.3*.8 = 3.146.

The profit must be greater than 3.146. n) 1.38 + 3 = 4.38

Allowable increase + Objective function. o) The profit will decrease by shadow price. p) No effect, the solution will be multi-optimal.