Setting Up the LP Problem

Setting Up the LP Problem

The following problem is developed from the area of chemical or petroleum engineering. However, it is relevant to all areas of engineering that deal with producing products with limited resources. Suppose that a gas-processing plant receives a fixed amount of raw gas each week. The raw gas is processed into two grades of heating gas, regular and premium quality. These grades of gas are in high demand (that is, they are guaranteed to sell) and yield different profits to the company. However, their production involves both time and on-site storage constraints. For example, only one of the grades can be produced at a time, and the facility is open for only 80 hr/week. Further, there is limited on-site storage for each of the products. All these factors are listed below (note that a metric ton, or tonne, is equal to 1000 kg):


Resource Availability
Raw gas
7 m3/tonne
11 m3/tonne
77 m3/week
Production time
10 hr/tonne
8 hr/tonne
80 hr/week
9 tonnes
6 tonnes


Develop a linear programming formulation to maximize the profits for this operation.