Consider the following linear programming model.

Maximize $Z=50x_1+30x_2$

s$.$t$.$

$2x_1+3x_{2}15$

$-5x_1+2x_{2}3$

$x_{1}4$

$x_1-x_{2}3$

$x_1,x_{2}0$

$($Constraint $1)$

$($Constraint $2)$

$($Constraint $3)$

$($Constraint $4)$

$($Non$-$negativity constraints$)$

a$.$ Draw the graphical representation of the model indicating each constraint and the objective function clearly. Make sure that you clearly label all the constraints and the objective function.

b$.$ Give an upper bound on the number of corner point solutions of the problem by using the formula.

c$.$ Identify the feasible region on the graph.

d$.$ Identify all corner point solutions indicating how you determine them verbally, showing them on the graph and labeling them appropriately.

e$.$ Examining the corner point solutions on the graph, indicate whether each is feasible, infeasible, or inconsistent.

f$.$ Find the optimal solution$($s$)$ to the given model by using graphical method. Explain your steps in finding the optimal solution$($s$).$

g$.$ Draw the objective function contour on the graph where it is equal to optimal objective value.