# Optimal solution for this problem without using Excel

Can someone teach me how to formulate the Optimal solution for this problem without using Excel?

The constraints I figured out are:

Copper .2x1 + .3x2 >= 8

Zinc .2x + .25x2 >= 6

Magnesium .15x1 + .1x2 >= 5

What is the next step?

Blacktop Refining extracts minerals from ore mined at two different sites in Montana.

Each ton of ore type 1 contains 20% copper, 20% zinc and 15% magnesium.

Each ton of ore type 2 contains 30% copper, 25% zinc and 10% magnesium.

Ore type 1 cost $90 per ton.

Ore type 2 cost $120 per ton.

Blacktop would like to buy enough ore to extract at least 8 tons of copper, 6 tons of zinc, and 5 tons of magnesium in the least costly manner

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#### Solution Summary

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