Attempt
Let $x_1$ be the number of hours to produce product 1 during assembly and $x_2$ be the number of hours to produce product 1 during finishing. Notice that $\frac{1}{2} x_1 + x_2 $ is the number of product 1 units produced. Similarly, call $x_3$ and $x_4$ be the number of hours spent during assembly and finishing to produce product two. We see thtat the number of units of product 2 is $x_3 + 2 x_4$. We want to maximize profit. So, our objective function is
$$ z = 25 (0.5 x_1 + x_2) + 15 (x_3+2x_4) $$
subject to
$$ x_1 + x_3 \leq 120 $$
$$ x_2 + x_4 \leq 85 $$
$$ x_1,x_2,x_3,x_4 \geq 0 $$
To find a worth of an hour of assembly and an hour of finishing, do we need to find the dual solution? Since the dual varaibles (y_1,y_2) that corresponds to each constraint one measures hours of assembly and $y_2$ measures hours of finishing. But, what is the units of the dual objective? Am I on the right track?
Best Answer
I would use two variables, $z_1, z_2$ to be the number of chairs to be made
$$\max 25 z_1 + 15z_2$$
subject to
$$2z_1 + z_2 \le 120$$
$$z_1 + \frac12z_2 \le 85$$
$$z \ge 0$$
Notice that the finishing constraint is never active.