For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables.    Max Z = 500x + 300y Subject to:  4x + 2y <= 60 (1st constraint) 2x + 4y <=  48 (2nd constraint) x, y >= 0 (non-negativity)   Barahan Plus Chemicals, Inc. produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demand for the coming month, the company's management has specified that the combined production for products A and B must total at least 350 gallons. Separately, a major customer's order for 125 gallons of product A must be satisfied. Product A requires 2 hours of processing time per gallon while product B requires 1 hour of processing time per gallon, and for the coming month, 600 hours of processing time are available. Barahan Plus Chemicals' objective is to satisfy these requirements at a minimum total production cost. Production costs are ₽80 per gallon for product A and ₽120 per gallon for product B. Formulate a linear programming model that will find the minimum-cost production schedule.

For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. 

Max Z = 500x + 300y

Subject to: 

4x + 2y <= 60 (1st constraint)

2x + 4y <=  48 (2nd constraint)

x, y >= 0 (non-negativity)

Barahan Plus Chemicals, Inc. produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demand for the coming month, the company's management has specified that the combined production for products A and B must total at least 350 gallons. Separately, a major customer's order for 125 gallons of product A must be satisfied. Product A requires 2 hours of processing time per gallon while product B requires 1 hour of processing time per gallon, and for the coming month, 600 hours of processing time are available. Barahan Plus Chemicals' objective is to satisfy these requirements at a minimum total production cost. Production costs are ₽80 per gallon for product A and ₽120 per gallon for product B. Formulate a linear programming model that will find the minimum-cost production schedule. 

*additional note: philippine peso is used as currency :)*