Answer step by step $,$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$2>=0$

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

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

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

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

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

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

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

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