Solve the standard minimization problem using duality.
Minimize $C = 18 s + 29 t$
Subject to $$\begin{array} { l }
3 s + 2 t \geq 60 \
6 s + 3 t \geq 60 \
s \geq 0 , t \geq 0
\end{array}$$
A) $C = 360$ , $s = 20$ , $t = 0$
B) $C = 580$ , $s = 0$ , $t = 20$
C) $C = 290$ , $s = 0$ , $t = 10$
D) $C = 180$ , $s = 10$ , $t = 0$
E) $C = 650$ , $s = 20$ , $t = 10$

Question

Solve the standard minimization problem using duality.  
Minimize $C = 18 s + 29 t$  
Subject to $$\begin{array} { l } 
3 s + 2 t \geq 60 \
6 s + 3 t \geq 60 \
s \geq 0 , t \geq 0
\end{array}$$  
A) $C = 360$ , $s = 20$ , $t = 0$
B)  $C = 580$ , $s = 0$ , $t = 20$
C)   $C = 290$ , $s = 0$ , $t = 10$
D)  $C = 180$ , $s = 10$ , $t = 0$
E)  $C = 650$ , $s = 20$ , $t = 10$

Quizplus · Accepted Answer

To solve this using duality, we convert the given minimization problem into its dual maximization problem. The dual problem aims to maximize $W = 60y_1 + 60y_2$ subject to $3y_1 + 6y_2 \leq 18$ and $2y_1 + 3y_2 \leq 29$, with $y_1, y_2 \geq 0$. Solving the dual problem gives the values of $y_1$ and $y_2$ that maximize $W$, which corresponds to the minimum $C$ in the primal problem. The correct choice leads to the minimum cost $C$ that satisfies all constraints.

Solve the Standard Minimization Problem Using Duality C=18s+29tC = 18 s + 29 tC=18s+29t

Solve the Standard Minimization Problem Using Duality $C = 18 s + 29 t$