$4\mathrm{.}9-4.$ Consider the following problem.

Maximize $,Z=x_1-7x_2+3x_3,$

subject to

$2x_1+x_2-x_{3}4(resource1)$

$4x_1-3x_{2}2(resource2)$

$-3x_1+2x_2+x_{3}3,($ resource $3)$

and

$x_{1}0,x_{2}0,x_{3}0.$

D$,$I $($a$)$ Work through the simplex method step by step to solve the problem.

$($b$)$ Identify the shadow prices for the three resources and describe their significance.

C $($c$)$ Use a software package based on the simplex method to solve the problem and then to generate sensitivity information. Use this information to identify the shadow price for