A manufacturing company makes three types of office chairs: Model A, Model B, and Model C. The construction of each chair requires a process involving three departmental steps; material workup, assembly, and packaging. The three departments have a maximum of 30, 53, and 47 hours available each week, respectively. The information is summarized below. Model A Model B Model C Material Workup (hrs) 1 1 1 Assembly (hrs) 2 3 2 Packaging (hrs) 1 2 3 The per unit profit is $40 for Model A, $80 for Model B, and $70 for Model C Let x represent the number of Model A chairs made in a week, y represent the number of Model B made in a week, and z represent the number of Model C chairs made in a week. Let P represent the objective function, where the objective would be to maximize profits.
a) Determine the objective function.
b) Introduce slack variables and set up the initial simplex tableau.
c) Solve the system using the algebraic methods discussed in Section 4.1. Show every step!
d) Report your solution in terms of maximum profit and each variable.