Exercise 10. A chemical manufacturer produces three chemicals: A, B and C. These chemical are produced by two processes: 1 and 2. Running process 1 for 1 hour costs $4 and yields 3 units of chemical A, 1 unit of chemical B and 1 unit of chemical C. Running process 2 for 1 hour costs $1 and produces 1 units of chemical A, and 1 unit of chemical B (but none of Chemical C). To meet customer demand, at least 10 units of chemical A, 5 units of chemical B and 3 units of chemical C must be produced daily. Assume that the chemical manufacturer wants to minimize the cost of production. Develop a linear programming problem describing the constraints and objectives of the chemical manufacturer. [Hint: Let x
1 be the amount of time Process 1 is executed and let x
2be amount of time Process 2 is executed. Use the coecients above to express the cost of running Process 1 for x
1 time and Process 2 for x 2 time. Do the same to compute the amount of chemicals A, B, and C that are produced.]