HINT

Part b

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$H$$5$ Available X$177\mathrm{.}8947368403012\mathrm{.}857147\mathrm{.}5$

$I$$5$ Available X$263\mathrm{.}1578947401554\mathrm{.}5$

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R$.$H$.$ Side Increase Decrease

$J$$10$ Dept A Hours Used $10015\mathrm{.}78947368100202\mathrm{.}454545455$

$J$$11$ Dept B Hours Used $3647\mathrm{.}36842105360\mathrm{.}6279076$

$J$$12$ Dept C Hours Used $47\mathrm{.}157894740501$E$+302\mathrm{.}842105263$

Part c

Let xA $=$ hours of overtime in Dept. A

xB $=$ hours of overtime in Dept. B

xC $=$ hours of overtime in Dept. C

Parameters

Hours$/$Unit Labor Hours OT Hours OT Max $30$x$1+15$x$218$xA $22\mathrm{.}5$xB $12$xC

Dept. Product $1$ Product $2$ Available Available Cost$/$Hr$.$ s$.$t$.$

A $10\mathrm{.}3510010$ $$18\mathrm{.}00$ x$1+0\mathrm{.}35$x$2$ xA $100$

B $0\mathrm{.}30\mathrm{.}2366$ $$22\mathrm{.}500\mathrm{.}30$x$1+0\mathrm{.}20$x$2$ xB $36$

C $0\mathrm{.}20\mathrm{.}5508$ $$12\mathrm{.}000\mathrm{.}20$x$1+0\mathrm{.}50$x$2$ xC $50$

Profit$/$Unit $$30\mathrm{.}00$ $$15\mathrm{.}00$ xA $10$

xB $6$

Model xC $8$

x$1,$ x$2,$ xA$,$ xB$,$ xC $^30$

Product $1$ Product $2$

Production $87\mathrm{.}2093023365\mathrm{.}11627907$

Dept. Total Hours Used OT Used Regular Hours Used

A #REF! $10$ #REF!

B #REF! $3\mathrm{.}186046512$ #REF!

C #REF! $0$ #REF!

Total Profit $$3,341\mathrm{.}34$

Shadow price means the marginal contribution of one additional unit of the

resource and its impact on the objective value $($profit$)$

Marginal value of Labor:

Dept A $$15\mathrm{.}80=$ Ever additional hour of over time can add to the profit,

$$15\mathrm{.}80$

Dept B $$47\mathrm{.}37=$ Ever additional hour of over time can add to the profit,

$$47\mathrm{.}37$

Dept C $$0$ or we cannot use any additional overtime because we already

have excess or unused labor hour.

The beige color, shows labor hours used. Dept A and B used all available

times. Dept C still has $50-47\mathrm{.}15=2\mathrm{.}85$ hours unused.HINT

Part b

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$H$$5$ Available X$177\mathrm{.}8947368403012\mathrm{.}857147\mathrm{.}5$

$I$$5$ Available X$263\mathrm{.}1578947401554\mathrm{.}5$

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R$.$H$.$ Side Increase Decrease

$J$$10$ Dept A Hours Used $10015\mathrm{.}78947368100202\mathrm{.}454545455$

$J$$11$ Dept B Hours Used $3647\mathrm{.}36842105360\mathrm{.}6279076$

$J$$12$ Dept C Hours Used $47\mathrm{.}157894740501$E$+302\mathrm{.}842105263$

Part c

Let xA $=$ hours of overtime in Dept. A

xB $=$ hours of overtime in Dept. B

xC $=$ hours of overtime in Dept. C

Parameters

Hours$/$Unit Labor Hours OT Hours OT Max $30$x$1+15$x$218$xA $22\mathrm{.}5$xB $12$xC

Dept. Product $1$ Product $2$ Available Available Cost$/$Hr$.$ s$.$t$.$

A $10\mathrm{.}3510010$ $$18\mathrm{.}00$ x$1+0\mathrm{.}35$x$2$ xA $100$

B $0\mathrm{.}30\mathrm{.}2366$ $$22\mathrm{.}500\mathrm{.}30$x$1+0\mathrm{.}20$x$2$ xB $36$

C $0\mathrm{.}20\mathrm{.}5508$ $$12\mathrm{.}000\mathrm{.}20$x$1+0\mathrm{.}50$x$2$ xC $50$

Profit$/$Unit $$30\mathrm{.}00$ $$15\mathrm{.}00$ xA $10$

xB $6$

Model xC $8$

x$1,$ x$2,$ xA$,$ xB$,$ xC $^30$

Product $1$ Product $2$

Production $87\mathrm{.}2093023365\mathrm{.}11627907$

Dept. Total Hours Used OT Used Regular Hours Used

A #REF! $10$ #REF!

B #REF! $3\mathrm{.}186046512$ #REF!

C #REF! $0$ #REF!

Total Profit $$3,341\mathrm{.}34$

Shadow price means the marginal contribution of one additional unit of the

resource and its impact on the objective value $($profit$)$

Marginal value of Labor:

Dept A $$15\mathrm{.}80=$ Ever additional hour of over time can add to the profit,

$$15\mathrm{.}80$

Dept B $$47\mathrm{.}37=$ Ever additional hour of over time can add to the profit,

$$47\mathrm{.}37$

Dept C $$0$ or we cannot use any additional overtime because we already

have excess or unused labor hour.

The beige color, shows labor hours used. Dept A and B used all available

times. Dept C still has $50-47\mathrm{.}15=2\mathrm{.}85$ hours unused.