A car dealer selects his cars for sale very carefully so as to ensure optimization of his profits. He deals in 4 types of cars A, B, F and G. The purchase value of the cars range at Rs. 60,000, 1,50,000, 55,000 and 2,20,000 and the sales value is fixed at Rs. 80,000, 1,75,00,75,000 and 2,50,000 respectively. The probability of sale are 0.8, 0.9, 0.6 and 0.50 respectively during a period of six months. In order to invest Rs. 20,00,000 in his deals, he wishes to maintain the rates of purchase of cars as 3 : 1 : 2 : 4. Work out how and how much he should buy. Formulate this problem as LP model.