The sensitivity report of a particular linear programming problem $($profit

maximisation$)$ is given as follows:

Adjustable cells

Cell

$C$$13$

$D$$13$

Name

Paint A

Objective

Final

value

$4$

Reduced

cost

coefficient

$0$

Paint B

Constraints

Cell

$E$$7$

Name

Raw Material X

$E$$8$

$E$$9$

$E$$10$

Raw Material Y

Demand S

$2$

Final

value

$24$

$6$

$0$

Shadow

price

$0\mathrm{.}75$

$5$

$4$

Constraint

R$.$H$.$S$.$

Allowable

increase

$1$

$6$

Allowable

increase

Allowable

decrease

$2$

$0\mathrm{.}6666667$

Allowable

decrease

$24$

$0\mathrm{.}51\mathrm{.}5$

Demand T

$1\mathrm{.}5$

$0$

$0$

$6$

$1$

$2$

a Regarding the linear programming problem, what is the optimal

solution?

$12$

$0\mathrm{.}6666667$

$1$E$+30$

$1$E$+30$

$(7$ marks$)$

b Suppose that the right$-$hand$-$side value of $$Raw Material X$$ changes

to $30,$ what can be said about the effect on the total profit? $(8$ marks$)$

c Suppose that the unit profit of $$Paint A$$ and $$Paint B$$ both decrease

by $0\mathrm{.}6,$ would the optimal solution change? If not, what is the

revised optimal profit that can be earned?