Please include the decision variables, objective function, and constraints.

A plant in a developing country can manufacture four different products in any combination. Each product requires time on each of three machines, as shown in the table below. All figures are in minutes per pound of product. Each machine is available 120 hours per week. Products A, B, C, and D are purely competitive, and any amounts made may be sold at per pound prices of $50,$43,$28, and $28, respectively. Variable labour costs are $30 per hour for machines 1 and 2 , and $60 per hour for machine 3 . Material costs are $5 for each pound of products A, B, C and D. 1. Formulate an LP model to help maximize total profit