Calculus Word Problem?

Question

When 30 orange are planted per acre each tree yields 150 oranges For each addtional tree per acre, the yield decreases by 3 oranges per tree. Express the total yield of oranges per acre, Y, as a function of the number of trees planted per acre, x, if x>/= 30.

Please help me explain the answer is Y=240x -3x^2. How do you get that?

Answer 1

So
If 31 trees/acre are planted, the yield per tree will be 150 - (3*1).
If 32 trees/acre are planted, the yield per tree will be 150 - (3*2).
If 33 trees/acre are planted, the yield per tree will be 150 - (3*3). And so on.

Now generalize. Suppose x trees per acre are planted. The number of trees by which this exceeds 30 is (x-30). Then the decrease in yield per tree is 3(x-30). So the yield per tree, if there are x trees, is 150 - 3(x-30), which simplifies to 240 - 3x.

Then the total yield Y per acre is the number of trees, times the yield per tree:

Y = x (240 - 3x) = 240x - 3x²