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

1. Ball point

2. Fountain pen

Weekly Net Profit = 700*3+133.33*5

= 2666.65

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

c) Unique

d) Marginal value is the same as shadow price

1. Chrome=0

2. Plastic= 1.1667

e) Yes, as the shadow price of steel is .8 and .6 is less. Then we will 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+3.33*5=1516.665

g) Shadow price of plastic is 1.17

Then allowable increase is 200

So net gain is 1.17*200=234

And the cost will be 1*500=500

So we should not buy.

h) 1.17*200=234 net gain

1*2(100) =200 cost

So yes the company should buy

The Optimal profit would be 3*1000+0+0 =Rs 3000

i) Shadow price is 6.5-6 =1.5*300=450gain

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

1.1*1.17+2*0+2*.8=2.887 cost

And the selling price is 3

l) Current profit =3

Decrease is =.78

The decrease 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.