The following linear programming problem has been solved by Excel's Solver. Use the output to answer the questions. Consider the following linear program:

MIN $12*1+10*2+9*3$

ST $5$ X$1+8$ X$2+5$ X$3>-608$ X$1+10$ X$2+5$ X$3>=80$

a$)$ What is the solution to the problem?

b$)$ Which constraints are binding?

c$)$ Interpret the reduced cost for x$1$

d$)$ What would happen if the cost of x$1$ dropped to $10$ and the cost of x$2$ increased to $127$

Final Value

Profit contribution

X$1$

$0$

$0$

X$2$

$8$

X$3$

$0$

$80$

$0$

Total

$80$

Variable Cells

Final Value

Reduced Cost

Objective Coefficient

Allowable. Increase

Allowable Decrease

Name

XI

$0$

$4$

$12$

IE$+30$

$4$

X$2$

$8$

$0$

$10$

$5$

$10$

X$3$

$0$

$4$

$9$

IE $+30$

$4$

Constraints

Final Value

Name

Shadow Price

Constraint R$.$H$.$ Side

Allowable Increase

Allowable Decrease

Constraint $1$

$64$

$0$

$60$

$4$

Constraint $2$

$80$

$1$

$80$

a$)$ According to the above equation, predict demand for months $2$ to $7$ by using exponential smoothing method with a$=0\mathrm{.}1$ and forecast for first month equal to $50.$