A fertilizer company makes a fertilizer using two chemicals that provide nitrogen ...

A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hrs of processing time on line 1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $ 6 per unit, and the profit for product 2 is $ 4 per unit.

a) Formulate a linear programming model for this problem.

a) Solve this model using graphical analysis

A fertilizer company makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium.  A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and 1 ounce of potassium.  Ingredient 1 cost $3 per pound, and ingredient 2 cost $5 per pound.  The company asked how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen 36 ounces of phosphate, and 2 ounces of potassium while minimizing cost.