Solve the following LP problem graphically 30 MARKS a A paint manufacturer produces two types of paint one type of standard quality SQ and the other of top quality TQ To make these paints he needs two ingredients the pigment and the resin Standard quality paint requires 2 units of pigment and 3 units of resin for each unit made and is sold at a profit of R1 per unit Top quality paint requires 4 units of pigment and 2 units of resin for each unit made and is sold at a profit of R150 per unit He has stocks of 12 units of pigment and 10 units of resin Formulate the above problem as a linear programming problem to maximize his profit 10 b Mr XYZ requires 1012 and 12 units of chemicals A B and C respectively for his garden The liquid product contains 52 and 1 units of A B and C respectively per jar The dry product contains 12 and 4 units of A B C per carton If the liquid product sells for R3 per jar and the dry product sells for R2 per carton how many of each should be purchased to minimize the cost and meet the requirements 10 c Minimise z 3x 2y subject to x 4y 8 5x 6y 30 y 4 x y 0