SOLUTION: how many units must be manufactured and sold to obtain this maximum, R(x)=160x-0.4x^2

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Question 1161431: how many units must be manufactured and sold to obtain this maximum, R(x)=160x-0.4x^2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

how many units must be manufactured and sold to obtain this maximum,
R%28x%29=160x-0.4x%5E2
R%28x%29=-0.4x%5E2%2B160x this is a parabola that opens down and its maximum is at vertex
so, rewrite equation in vertex form
R%28x%29=-0.4%28x%5E2-400x%29 ...complete square
R%28x%29=-0.4%28x%5E2-400x%2Bb%5E2%29-%28-0.4%29b%5E2
R%28x%29=-0.4%28x%5E2-400x%2B200%5E2%29%2B0.4%2A200%5E2
R%28x%29=-0.4%28x-200%29%5E2%2B0.4%2A40000
R%28x%29=-+0.4+%28x+-+200%29%5E2%2B16000
=> h=200 and k=16000
vertex is at (200,16000)
200 units must be manufactured and sold to obtain this maximum of 16000