4 Suppose a firm produces two goods, x and x2. Each requires three inputs: machine time, labour time and a single raw material. The amount of each input required to produce a unit of each output, together with the amount of inputs available, are given in the following table: Product Input available x1 x2 Machine time 3 3 18 Input Labour time 1 2 8 Raw material 2 1 10 Given that the profit contribution per unit of x, and x2 is 6 and 9 respec- tively, find the output combination that maximises profit, using the Simplex method. What assumptions are implicit in your answer?