Assignment:
A Cement Factory makes 2 grades of cement, A & B. the factory requires a minimum production quantity of 10000, and 12000 tons of grades A and B, respectively. Each ton of grade A is composed of 0.6 tons of ingredient 1, 0.3 tons of ingredient 2, and 0.1 tons of ingredient 3. The composition of grade B is 0.3, 0.2 and 0.5 tons of ingredients 1, 2, and 3 respectively. Each ton of grade A sells for $240 & costs $22 to manufacture. Grade B also costs $ 30 to manufacture but sells for $ 200/ ton. An ingredient 1 is available in unlimited quantity, but 2 & 3 are available only up to 14,000 and 20,000 tons, respectively. The cost/ton of ingredients 1, 2 and 3 is $ 80, $50 and $100 respectively. Formulate and solve a linear programming model to maximize profit.
Provide complete and step by step solution for the question and show calculations and use formulas.