A person produces two products chemicals, namely product A and product B. Both products are manufactured from the same raw material and processed by the same machine. The available machine capacity is 500 hours and 9000 kilogram of raw materials are available. The production of one unit of product chemicals A utilises 40 minutes of machine time while one unit of product B chemicals takes 2 hour to produce. To produce one unit of product A chemicals , 15.5 kg of raw material is required whereas 15 kg is required for one unit of product B chemicals. The marginal income of product A, of which a maximum of 800 units can be sold, amounts to R1 per unit. Product B has a marginal income of R2 per unit. The company wants to determine what combination of product A and product B must be produced in order to obtain maximum profit. Formulate a linear programming model for the above problem and hence find the optimal solution by using the simplex method.