SOLUTION: Steve opened a boutique in a shopping mall to sell
perfumes and cologne. The amount made by the store is given by the formula,
A = 50 (m - 8 )2 - 3200
where A is the amount
Question 1166724: Steve opened a boutique in a shopping mall to sell
perfumes and cologne. The amount made by the store is given by the formula,
A = 50 (m - 8 )2 - 3200
where A is the amount made by the store in dollars and m is the number of months the store has
been opened.
a. During what month did he have the lowest net and what was it?
b. What is the amount made after 18 month? Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! i believe your formula needs to be:
A = 50(m-8)^2-3200
the ^ symbol indicates exponentiation.
the * symbol indicates multiplication.
simplify it to get:
A = 50(m^2-16m+64)-3200
simplify further to get:
A = 50m^2 - 800m + 3200 - 3200
simplify further to get:
A = 50m^2 - 800m
set A equal to 0 to get:
0 = 50m^2 - 800m
the equation is now in standard form.
in that form:
a = coefficient of the m^2 term = 50
b is the coefficient of the m term = 800
the max/min point is when m = -b/(2a)]
that becomes m = 800/100 = 8
the quadratic equation is at a minimum/maximum when m = 8
since the coefficient of the m^2 term is positive, than m = 8 is a minimum point in the equation.
if the coefficient of the m^2 term was negative, then m = 8 would be a maximum point in the equation.
note that the normal standard form of a quadratic equation is ax^2 + bx + c = 0.
all that was done here was replace x with m.
the standard form then became am^2 + bm + c = 0.
the min/max equation that is normally x = -b/(2a) became m = -b/(2a).
your min point is when m = 8.
since the formula is A = 50 * (m - 8) ^ 2 - 3200, then the equation becomes -3200 when m = 8 because A = 50 * (8 - 8) ^ 2 - 3200 becomes A = 0 - 3200 which becomes A = -3200.
when m = 18, the formula becomes A = 50 * (18 - 8) ^ 2 - 3200 which becomes A = 50 * 10^2 - 3200 which becomes A = 5000 - 3200 which becomes A = 1800.
this can be shown on the following graph of the equation, where A is represented by y and m is represented by x.
