QUESTION 2 30 MARKS

GlowWell is a paint manufacturing company, It has formulations for two new brands of paint, Premium Plus and Ultra Hide. There are none of these in stock so they must be manufactured from scratch. A new order has come in and these two products has to be manufactured in 8 hrs. The two main ingredients in these paints are pigments and resins. The Premium brand requires 5mg of pigments and 0.2 mg of resins in each can of paint. The Ultra Hide brand requires 4mg of pigments and 0.1 mg of resins in each can of paint. These formulations stipulate that pigments must be no more than 100mg and resins must be no less than 3mg per can of paint. GlowWell requires 12 minutes to manufacture a can of Premium Plus and 48 minutes for a can of Ultra Hide. The company needs to know the combination of paints to maximise its revenue. GlowWell will sell a can of Premium Plus for $10 and a can of Ultra Hide for $15.

1. Use X₁ and X₂ to define the variables indicating which variable is X₁ and X₂

2 Marks

1. Derive GlowWell's Objective Function in terms of X₁ and X₂ 3 Marks

1. What are the Contraints under which GlowWell must operate 7 Marks

1. Graphically illustrate the Feasible Region 4 Marks

1. State the coordinates of the corner points e.g A(2,7), B(12,5) 8 Marks

1. Determine optimal solution 4 Marks

1. Determine the revenue at the optimal solution 2 Marks

NB. Please show working