A gold processor has two sources of gold ore, source A and source B. In order to keep the plant running, at least three tons of ore must be processed each day. Ore from sourc A costs 20 per ton to process, and ore from B cost 10 per process. Costs must be kept to less than 80 per day. Moreover require that the amount of ore from source B cannot exceed twice the amount of source A. The lab reports that ore from source A yields 2 oz of gold per ton, and ore from source B yields 3 oz of gold per ton. How many tons of ore from both sources must be proceeded each day to maximize the amount of gold extracted subject to the above constraints?

Graphically solve to show how many tons of ore should be processed from both sources to maximize the amount of gold extracted.


Thanks

I won't deprive you of the learning you would get if you managed to solve it yourself. However, I'll give you some hints.

A = amount of ore of A
B = amount of ore from B

Write down an equation for the cost of ore
Write down an equation for the yield.
Yield must be maximized, cost must be minimized (and <= 80)

The problem wants you to do it graphically so you can visually understand the result.

I won't deprive you of the learning you would get if you managed to solve it yourself. However, I'll give you some hints.

A = amount of ore of A
B = amount of ore from B

Write down an equation for the cost of ore
Write down an equation for the yield.
Yield must be maximized, cost must be minimized (and <= 80)

The problem wants you to do it graphically so you can visually understand the result.

max=2x + 3x

constraints
x1 + x2 >= 3
20x1 + 10x2<=80
2x1>=x2