Using an Excel solver, solve the following LP problem.

x$\_1=$ number of necklaces to be made

x$\_2=$ number of bracelets to be made

x$\_3=$ number of ear$-$studs to be made

Maximize Profit $($Z$)=60$ x$\_1+40$ x$\_2+20$ x$\_3($currency used is in dollars$)$

Subject to

$4$x$\_1+3$x$\_2+2$x$\_3<=50$ availability of gold

$2$x$\_1+4$x$\_2+1$x$\_3<=40$ availability of platinum

x$\_1<=5$ demand necklace

x$\_3=3$ demand ear studs

x$\_1,$x$\_2,$x$\_3>=0($Non$-$negativity constraint$)$

Note that fractional values for the variables are acceptable. Use two decimal places to provide answers to questions $4$ through $8$

$1.$ Generate Input Sheet $5$ marks

$2.$ Answer report $7\mathrm{.}5$ marks

$3.$ Sensitivity report $7\mathrm{.}5$ marks

Each of the following questions carries four marks. $5*4=20$ marks

$4.$ What are the binding resources mentioned in the problem? Explain each of these in a sentence or two.

$5.$ What is the reduced cost of the necklace? Show your calculations. Also, explain the significance of reduced cost in the business context.

$6.$ What is the new profit if the profits from necklaces increase by $$10$ and the bracelet increases by $$10?$ Show all your steps and explanation

$7.$ What is the new profit if you add five units of gold and remove $($reduce$)5$ units of platinum?

$8.$ What are the upper and lower limits of objective coefficients?