Question

1. Tizzoola manufactures two electric SUVs, the Expedient and the Fiori. The firm’s new manufacturing plant will build both vehicles and run 24 hours per day. Two departments (paint shop and final assembly) are critical to production and have limits on time available. A Fiori requires 1/40 of a day in the paint shop and 1/50 of a day in assembly. An Expedient require 1/50 of a day in the paint shop and 1/50 of a day in assembly. An Expedient yields profit of $5000 and a Fiori yields $3000 in profit.

   1. Define (list) the variables.

   2. Define the objective function and constraints.

   3. Graph the feasible region.

   4. What should be the plant’s daily production plan for maximum profit (optimal number to produce)?

   5. What is the maximum profit if the firm produces the optimal product mix?

Answer 1

The decision variable

x = number of Expedients

y = number of Fioris

The objective function

Maximize 5000x + 3000y

Constraints

(1/50)x + (1/40)y <= 1

(1/50)x + (1/50)y <= 1

Or

0.48x + 0.6y <= 24

0.48x + 0.48y <= 24

Final set of constraints can be written as

0.48x + 0.6y <= 24

0.48x + 0.48y <= 24

x, y >= 0

Graph of the feasible region is shown below. The area marked in red is the feasible region.

The corner points are (0,0), (50,0) and (0,40). We see that the maximum value will be at (50,0). Thus the plant should make x = 50 and y = 0. In other word the plant should produce 50 Expedients and 0 Fiori to maximize profit.

The total profit at optimal solution will be 50*5000 = 250000.

We assume that all the cars manufactured will be sold