Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP

problem:

Maximize contribution $=,6x_1+8x_2+4x_3$

$,1x_1+7x_2+4x_{3}72$

$,2x_1+1x_2+7x_{3}76$

$,8x_1+4x_2+1x_{3}72$

$,x_1,x_2,x_{3}0$

$(C_1$ : hours on machine $1)$

$(C_2$ : hours on machine $2)$

: hours on machine $3)$

a$)$ Using a computer software for solving LP$,$ the optimal solution achieved is:

$x_1=$

$($round your response to two decimal places$).$

$x_2={?}_{{?}_{?}}{?}_{}(round$ your response $to$ two decimal places$)$

x3=?__(roundyourresponsetotwodecimalplaces)

Contribution(objectivevalue)=__(roundyouranswertoteodecimalplaces)

b)machine1has__hoursofunusedtimeavailableattheoptimalsolution(roundyourresponsetotwodecimalplaces)

Machine2has__hoursofunusedtimeavailableattheoptimalsolition(roundyourresponsetotwodecimalplaces)

Machine3has__hoursofunusedtimeavailableattheoptimalsolution(roundyourresponsetotwodecimalplaces)

c)Anadditionalhouroftimeavailableforthirdmachine,isworth__dollarstothefirm(roundyourresponsetotwodecimalplaces)

Pleaseanswerall