How to solve

$(4)$ BC manufactures two types of wooden toys: soldiers and trains. Each soldier sells for $$39$ and uses $$19$ worth of

raw materials. Each soldier that is manufactured increases BC$\text{'}$s variable labor and overhead costs by $$12.$ Each

train sells for $$32$ and uses $$7$ in raw materials, with an additional $$19$ in variable labor and overhead costs per unit.

The production of both toys requires two types of skilled labor: carpentry and finishing. Manufacturing a soldier

requires $5$ hours of finishing labor and $4$ hours of carpentry labor, while a train needs $3$ hours of finishing labor and

$2$ hours of carpentry labor. Each month, BC can obtain all the needed raw material but only $4,000$ finishing hours

and $3,000$ carpentry hours. Monthly demand for soldiers is at most $100$ units, while demand for trains is $200$ or

more units. Formulate an LP model that helps BC to maximize monthly profit $($revenues $-$ costs$).$

$($a$)$ Step $1$: Define the decision variables precisely and completely. That is$,$ Let $x_1=$

and $x_{{?}_{?}}(2)=$

etc.

$($b$)$ Step $2$: State the objective function.

$($c$)$ Step $3$: Specify the constraints.

$(5)$ Consider the following linear programming model with $4$ regular constraints:

Maximize $6x+10Y$

subject $to$: $2x+1Y20(constrain\frac{t}{\text{\#}}1)$

$4x+4Y48(constraint\frac{?}{?}$#$2)$

$4x+3Y50(constraint\frac{?}{?}$#$3)$

$x2(constraint\frac{?}{?}$#$4)$

$x,Y0(non-$negativity constraints$)$

$($a$)$ Which of the constraints is redundant? Constraint #

$($a$)$ Draw your graph in the space below: