Sharon's revenue R (in dollars) on the sale of x fruitcakes is determined by the formula R= 50x - x^2. Her cost C ( in dollars) for producing x fruitcakes is given by the formula C = 2x + 40. For what values of x is Sharon's profit positive? (Profit = revenue - cost.)
2007-08-11 18:38:01 · 3 answers · asked by Javid M 1 in Science & Mathematics ➔ Mathematics
We have profit = (50 - x^2) - (2x + 40, or P = -x^2 + 48x - 40. This is a parabola which opens down, so P will be positive when x is between the intercepts. We find the intercepts using the quadratic formula, so P > 0 when
(-48 + sqrt(48^2 -160))/(-2) < x < (-48 - sqrt(48^2 - 160))/(-2) , or approximately when 0.85 < x < 47 .
2007-08-11 18:57:16 · answer #1 · answered by Tony 7 · 0⤊ 0⤋
R-C = 50x-x^2-(2x+40)>0
x^2-48x+40<0
x < 24+√2144, x is a positive number
2007-08-11 18:48:07 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋
ok i think this could desire to be the nicely suited formula for extensive form one, yet you will could desire to make certain the respond. p=15 human beings, x=form of extra human beings. p+x=50-2x so 15 human beings plus how ever many extra is comparable to $50 minus $2 cases the quantity of what number extra human beings.
2016-10-10 01:13:56 · answer #3 · answered by lambdin 4 · 0⤊ 0⤋