Best Way to Form an Equation On This Optimisation Question?

[Procrastinate]

An orchardist has one grove of 50 orange trees. Each tree produces 800 oranges. The orchardist knows from experience that each addition tree planted in the grove will reduce the output of each tree by .10 oranges. How many tree should the orchardist plant in the grove in order to maximize the total population?



I am just wondering if there are any good tips on finding an equation for this question. I want to improve my problem solving skills but I can't understand how the answer was found (800-(x-50)x) or something similar (I don't have my solutions on me.)

I don't need to know how to solve it.

Thanks.

 

[HallsofIvy]

An orchardist has one grove of 50 orange trees. Each tree produces 800 oranges. The orchardist knows from experience that each addition tree planted in the grove will reduce the output of each tree by .10 oranges.

So the number of oranges produced by each tree, if there are "x" more trees planted, is 800- .10x.

How many tree should the orchardist plant in the grove in order to maximize the total population?



I am just wondering if there are any good tips on finding an equation for this question. I want to improve my problem solving skills but I can't understand how the answer was found (800-(x-50)x) or something similar (I don't have my solutions on me.)

I don't need to know how to solve it.

Thanks.

If x more trees are planted, there will be 50+ x trees. The total number of oranges is, of course, "oranges per tree" times "number of trees"- (800- .10x)(50+ x).