One of PLE's manufacturing facilities produces metal engine housings from sheet metal for both mowers and tractors. Production of each product consists of five steps: stamping, drilling, assembly, painting, and packaging to ship to its final assembly plant.

The production rates in hours per unit and the number of production hours available in each department are given in the following table:

Department

Mower Housings

Tractor Housings

Production Hours Available

Stamping

0.03

0.07

200

Drilling

0.09

0.06

300

Assembly

0.15

0.10

300

Painting

0.04

0.06

220

Packaging

0.02

0.04

100

.

.

In addition, mower housings require 1.2 square feet of sheet metal per unit and tractor housings require 1.8 square feet per unit, and 2,500 square feet of sheet metal is available.

.

The company would like to maximize the total number of housings they can produce during the planning period.

Formulate and solve a linear optimization model and recommend a production plan.

Illustrate the results visually to help explain them in a presentation to Ms. Burke. In addition, conduct whatever what-if analyses (e.g., run different scenarios and apply parameter analysis) you feel are appropriate to include in your presentation.