Q3 A company produces 3 types of paint. For 1 unit of paint-1, 8 units of pigment, 4 units of resin and 2 units of solvent is required. For 1 unit of paint-2, 2 units of pigment, 8 units of resin and 4 units of solvent is required. For 1 unit of paint-3, 4 units of pigment, 2 units of resin and 8 units of solvent is required.
Answer the following questions independently.
a) If there are only 16 units of pigment, 22 units of resin and 18 units of solvent is available daily. Formulate system of equations to find number of units of paint 1, 2 and 3 that can be produced daily with using exact amount of available raw materials. Solve the system of equations using LU decomposition. (9 marks)
b) The manpower required for producing 1 unit of paint-1, paint-2 and paint-3 are 4, 3 and 4 units respectively and profit of Rs 20, Rs 10, Rs 15 are made by selling single unit of paint-1, paint-2 and paint-3 respectively. The manpower available is 25 per day. At most 18 units pigment and at most 25 units of resin can be used daily whereas at least 15 units of solvent should be used for production. Formulate an LPP to find the number of units of paint-1, paint-2, and paint-3 that can be produced daily so as to maximize the profit assuming the product made can be sold on daily basis with exact usage of manpower. (No Need to solve the LPP). (3 marks)
Mathbot Says...
I wasn't able to parse your question, but the HE.NET team is hard at work making me smarter.