Required: $)$Find the Z Value$)$ Use a linear programming solver or method to find x$1,$x$2,$x$3,$x$4$ that maximize Z$.$The Z value represents the maximum profit considering the given constraints and requirements. Question: The Bean Barn needs to grind the beans to make three types of house special coffee blends. There are four types of coffee beans used to make the three blends. The three coffee blends are mellow mocha, regular and java jolt. The four types of beans available are Vietnamese, Columbian, Blue Mountain & Brazilian. Any un$-$used beans will be used in other products. The requirements for the three coffee blends are as follows:

The Blends

Blend

Mellow

Regular

Java Jolt

Min Ph $4\mathrm{.}64\mathrm{.}64\mathrm{.}6$

Min caffeine $\%$ none $1\mathrm{.}5\%2\mathrm{.}6\%$

Max caffeine $\%1\mathrm{.}2\%2\mathrm{.}5\%$ unlimited

Max we can sell $100$ lbs$.200$lbs$.150$lbs$.$

Selling Price$/$Lb $$10$ $$15$ $$20$

The Beans

Bean

VN

CO

BM

BZ

Ph

$4\mathrm{.}2$

$4\mathrm{.}8$

$5\mathrm{.}0$

$4\mathrm{.}5$

Caffeine $\%$

$3\%$

$\mathrm{.}8\%$

$2\mathrm{.}7\%$

$3\mathrm{.}1\%$

Lbs$.$ available

$125$

$150$

$150$

$175$

Cost$/$Lb$.$

$$6$

$$9$

$$12$

$$8$