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# Mathematics - Linear Operators

Please help with solving this problem in graphical analysis and formulate a linear programming model for the below:

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

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 cs \$3 per pound, and intredien 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 phosphae, and 2 ounces of potassium while minimizing cost.

I am having trouble with graphing these. Please help graph and explain.

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file.

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