please use 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 Turquoise 0 0 0 15 45 85 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? Instructions Questions 1 and 2 are to be done by hand, showing all the steps needed to derive the answers. [Of course, you could use LINGO or the Excel Solver to verify your answers, but this is not to be submitted.] Use Word or pdf for this question; if making the solutions with cursive writing, please be neat. For Questions 3 and 4, a computer-based sensitivity analysis needs to be performed. For each question, on LINGO you need a file for the model, the solution report, and the range report. For Excel, one file with nine tabs can be used; for each of the three questions, there is the model, the Answer Report, and the Sensitivity Report. Use Word or pdf to give the answers to the sensitivity questions. For each give part, write a couple of sentences; don't just submit a numerical