Solve the following linear programming problem. Complete parts$($a$)$ through$($d$).$

Minimize

wequals$5$ y $1$ plus y $2$

subject to

$4$ y $1$ plus

$5$ y $2$

greater than or equals$20$

$4$ y $1$ plus

y $2$

greater than or equals$24$

with

y $1$greater than or equals$0,$ y $2$greater than or equals$0$

Question content area bottom

Part $1$

$($a$)$ Write the dual.

Maximize

zequals

$$

enter your response herex $1$plusleft parenthesis nothing right parenthesis

$$

x $2$

subject to

$$

enter your response here

less than or equals$5$

$$

enter your response here

less than or equals$1$

with

x $1$greater than or equals$0,$ x $2$greater than or equals$0$

$($Do not$$ factor.$)$

$($b$)$ Write the initial simplex tableau.

x $1$

x $2$

s $1$

s $2$

z

$4$

$$

enter your response here

$1$

$$

enter your response here

$0$

$$

enter your response here

$$

enter your response here

$1$

$0$

$$

enter your response here

$0$

$$

enter your response here

$$

enter your response here

$$

enter your response here

$0$

$0$

$1$

$$

enter your response here

$($c$)$ Find the final simplex tableau.

x $1$

x $2$

s $1$

s $2$

z

$$

enter your response here

$0$

$1$

$$

enter your response here

$0$

$$

enter your response here

$$

enter your response here

$1$

$$

enter your response here

$1$

$0$

$$

enter your response here

$$

enter your response here

$0$

$0$

$$

enter your response here

$1$

$$

enter your response here

$($Simplify your$$ answers.$)$

$($d$)$ Read the solution from the final simplex tableau.

The minimum is wequals

$$

enter your response here when y $1$equals

$$

enter your response here and y $2$equals

$$

enter your response here.

$($Simplify your$$ answers.$)$

input field $1$input field $2$input field $3$input field $4$input field $5$input field $6$input field $7$input field $8$input field $9$input field $10$input field $11$input field $12$input field $13$input field $14$input field $15$input field $16$input field $17$input field $18$input field $19$input field $20$input field $21$input field $22$The minimum is wy $1$when y $1$y $2$and y $2($Simplify your answers.$)$