One of PLE’s manufacturing facilities produces metal engine housings from sheet metal for both mowers and tractors. Production of each product consists of three steps: stamping, assembly, and painting to ship to its final assembly plant. The production rates in hours per unit and 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
Assembly 0.15 0.10 300
Painting 0.04 0.06 220
In addition, mower housing 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.
a. Identify the decision variables, objective function, and constraints in simple verbal expressions.
b. Mathematically formulate a linear optimization model.