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The mathematical statement of a problem and its excel solution are given as follows :

S$.$t$.$

Zmax$=8101+7002+5203$

$41+32+3360(labour,hr)$

$21+42+5350(fabric)$

$1+32+2350(painting)$

$1,2,30$

Here note that the number $E+..$ is a very large number which can be accepted as an infinite number.

Please answer the questions according to theLINDO data given below.

a$)$ Indicate the basic and non$-$basic variables, and their quantities at the optimal tableau in the excel sheet.

b$)$ Indicate the binding and nonbinding constraints of the problem at the optimal solution. Explain your

answer.

c$)$ Indicate the amount of the resources to be used at the optimal solution. Explain your answer? d$)$ Indicate the objective function coefficient of $\backslash$times $2.$ Interpret the meaning of the number.

e$)$ Indicate the technological coefficients of $\backslash$times $1$ at the first constraint. Interpret the meaning of the number.

f$)$ Indicate the optimality range of x$2.$ If we increase the objective function coefficient of x$2$ to $1000,$ how does

the value of the variables and the value of Z change?

g$)$ Indicate the feasibility range of the painting constraint, and interpret this range.

h$)$ What is the shadow price of the first constraint? How does it affect to value of Z $?$ Explain your answer.

Find variables that are not in the model. For each one explain what would be its contribution to the optimal

objective function value if a unit of the variable was in the model?

i$)$ Factory managers want to produce more products by overtime in the first constraint, labour. Overtime in

this resources costs the company $$120$ per hour. In this case, should the company accept this? Explain your

idea.

j$)$ What would be the shadow price if we decrease the fabric to $29$ hours? Explain.