a firm manufactures two types of paint: emulsion and gloss. the profit contribution for each product is: $4 per emulsion and $6 per gloss. both products are processed on the three machines: M1, M2 and M3. the time required for each product and the total time available per week on each machine is as follows: machines M1, M2, M3, emulsion (hours) 2, 2, 4, gloss (hours) 2, 4, 10 and available hours per week: 22, 54, 180. A. write down the objective function and all the constraints