OBJECTIVE FUNCTION VALUE $1100\mathrm{.}00$

VARIABLE

VALUE

REDUCED COST

XI

$33\mathrm{.}333$

$0\mathrm{.}000$

X$2$

$266\mathrm{.}667$

$0\mathrm{.}000$

CONSTRAINT

SLACK$/$SURPLUS

SHADOW$/$DUAL PRICES

$123$

$33\mathrm{.}333$

$0\mathrm{.}000$

$0\mathrm{.}000$

$1\mathrm{.}000$

$3$

$0\mathrm{.}000$

$10\mathrm{.}000$

OBJECTIVE COEFFICIENT RANGES

VARIABLE

X$2$

CURRENT VALUE

UPPER LIMIT

LOWER LIMIT

$3\mathrm{.}500$

$5,000$

$3\mathrm{.}125$

$3\mathrm{.}500$

RIGHTHAND SIDE RANGES

$5\mathrm{.}600$

$5\mathrm{.}000$

CONSTRAINT

$3$

LOWER LIMIT

CURRENT VALUE

$316\mathrm{.}667$

$350\mathrm{.}000$

$200\mathrm{.}000$

$300\mathrm{.}000$

$75\mathrm{.}000$

$80\mathrm{.}000$

UPPER LIMIT

NO UPPER LIMIT

$320\mathrm{.}000$

$90\mathrm{.}000$

a$)$ What are the optimal values of X$1$ and X$23(2$ Marks$)$

X$=33/333$

b$)$ The maximum profit? $(1$ Mark$)$

$246-67$

c$)$ What is the minimum contribution by X$1$ that will maintain the same optimal solution?

$(2$ Marks$)$

d$)$ Suppose C$2$ changed from Sh$.3,5$ to Sh$.6$ will the current optimal solution change?

e$)$ Suppose CI changed from Sh: $5$ to Sh$.4$ and C$2$ changed from Sh$.3\mathrm{.}5$ to Sh$.$

$(3$ Marks$)$

simultaneously, evaluate whether the current optimal solution will change. $(4$ Marks$)$ f$)$ Suppose extra material can be acquired at Sh$.8$ per unit, is it worthwhile? Explain

$9)$ Suppose simultaneously material increases by $100-$units, packaging boxes increase by $10$