Question # $1$: $(32$ points$)$

Consider the following LP model:

Max Z$=5$X$1+3$X$2$

S$.$T$.$ X$1+$X$2<=4($resource $1)$

$5$X$1+2$X$2<=10($resource $2)$

$3$X$1+2$X$2<=9($resource $3)$

X$1,$X$2>=0$

a$-$ Plot the constraints and identify the feasible solution space.

b$-$ What are the optimum values of the variables?

c$-$ Give $2$ values of the variables that are feasible $($not necessarily optimal$)$

d$-$ What is the optimum value of the objective function?

e$-$ What is the maximum allowable increase in resource $1?$

f$-$ Compute the unit worth for all the resources.

g$-$ Which resource should be given priority to increase? Why?

h$-$ Determine the range of objective function coefficients ratio that will keep the optimum value in part d unchanged?

j$-$ Identify the types of constraints, and the status of each resource.

k$-$ Identify the solution space if each of the following changes is effected separately:

$1-$ The first constraint becomes X$1+$X$2>=4$

$2-$ The second constraint becomes $5$X$1+2$X$2>=10($solve on apaper please$)$