Question

1. Here's a portion of the sensitivity analysis for the constraints. Answer the following questions.

Cell	Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
$E$10	Bar/Food	0	1560	0	5	16
$E$11	Budget	150000	3.4	150000	1E+30	96200
$E$6	Excursions	24.24	0	5	19.24	1E+30
$E$7	Restaurant	12	-1660	12	16

1. What happens to the optimal solution if you can get more budget? How much more of the budget can you get? [10 Marks]
2. What happens to the optimal solution if the excursions resource is increased to 25? [5 Marks]
3. Interpret the -1660 shadow price for restaurant resource. [5 Marks]

Answer 1

a.The optimal solution does not change when the RHS of the budget constraint increases.The shadow price of budget constraint=3.4

A shadow price indicates by how much the optimal increases or decreases when the RHS of the constraint increases by 1 unit.Hence,when the budget is increased,the optimal solution increases by ,

Increase in optimal solution=Shadow price*Number of units =3.4*Number of units

Allowable increase for the budget constraint=Infinity.

Hence,the budget can be increased to infinity.

b.The optimal solution changes because the allowable increase for the excursions constraint =5+19.24=24.24

So,the solution does not remain optimal when the RHS is increased to 25.

c. The shadow price for restuarant constraint is -1660 which indicates that the optimal solution value decreases by 1660 for every 1 unit increase of the RHS of the restaurant constraint.