Maths Solve the Following Question.(4 Marks)

A horticulturist wishes to mix two brands of fertilizers that will provide a minimum of 15 units of potash, 20 units of nitrate and 24 units of phosphate. One unit of brand I provides 3 units of potash, 1 unit of nitrate, 3 units of phosphate. One unit of brand II provides 1 unit of potash, 5 units of nitrate and 2 units of phosphates. One unit of brand I costs Rs. 120 and one unit of brand II costs Rs.60 per unit. Formulate this problems as L.P.P. to minimize the cost.

A Toy manufacturer produces bicycles and tricycles, each of which must be processed through two machine A and B. Machine A has maximum of 120 hours available and machine B has a maximum of 180 hours available. Manufacturing a bicycle requires 4 hours on machine A and 10 hours on machine B. Manufacturing a tricycle required 6 hours on machine A and 3 hours on machine B. If profits are Rs.65 for a bicycle and Rs.45 for a tricycle, formulate L.P.P. to have maximum profit.

Find the graphical solution of 3x + 4y ≤ 12, and x - 4y ≤ 4.

Find the common region of the solutions of the inequations x + 2y ≥ 4, 2x - y ≤ 6.