Please only take 11 variables and solve in LINGO.

4. (25 marks) A paint blending operation buys paint in five colours. These are white, black, and the three primary colours of red, blue, and yellow. There are five vats in which to receive these colours from the supplier; the white vat and the black vat each has a capacity of 5000 litres. Each primary colour vat has a capacity of 25,000 litres. All paint regardless of colour is purchased at a price of $9 per litre. Each product is made as a specified percentage of the five basic paints. Here is the list of their products: Percentages of the Five Basic Paints Name of the Product White Black Red Blue Yellow Candy Cane 20 0 70 10 0 Hunter Green 0 15 0 25 60 Passion Purple 0 10 50 40 0 Olive Green 0 0 5 20 75 Sunset Orange 5 0 50 0 45 Turquoise 0 0 0 85 15 There are also six vats for the products. For each of the six products, there is a dedicated 15,000 litre capacity vat. All these products are sold at a price of $12 per litre. Assume that no paint is lost in the blending process. (a) Give the algebraic model for this situation. (Hint: only 11 variables are needed.) (b) Solve this model in LINGO or the Excel Solver, and obtain the sensitivity re- port. (c) The plant management could seek some funds which could be used to expand the capacity of one or more of the 11 vats. Spreading out such costs over time would work out to a price of about $2.00 per litre to expand any of the 11 vats. Based on the information which could be gleaned from the sensitivity re- port(s) alone, and considering several possibilities, what would you recommend to management