Question Two

You are the finance manager of the firm Sunderland Plastics Limited, which produces two products (X1 and X2) using two different machines (M1 and M2). Each unit of X1 requires 4 hours of processing time on M1 and 2 hours of processing time on M2. Each unit of X2 that gets produced requires a 1 hour processing time on M1 and 1.5-hour processing time on M2. The firm has an available processing time of 40 hours of M1 and 30 hours of M2 available this week. The firm also meets the non-negativity constraints. Your task is the following: The firms makes a net profit of 400 USD from 1 unit of product X1 and 100 USD from 1 unit of product X2 1) Formulate a linear programming problem in the standard form for Sunderland Plastics Limited. 2) Solve the problem graphically and show what combination of the products X1 and X2 the firm should produce to maximise its profit while satisfying the constraints it is facing. How much profit will the firm make?