Problem $5$:

A furniture firm produces three outputs chairs, tables, and desks. Production of the output requires inputs

labor $(x_1)$ and wood $(x_2).$ The firm's objective is to minimize the cost of meeting the three production

constraints.

$\frac{m}{i}nTC=10x_1+40x_2$

$s.t.$

$2x_1+8x_{2}40(chairs)$

$3x_1+9x_{2}36(tables)$

$8x_{1}32(desks)$

$x_1,x_{2}0$

Solve and graph the primal problem given above. State the optimal values for $x_j$ and $s_i,$ as well as TC$.$