What is the number of $1 reductions that will result in the greatest revenue and explain your reasoning?
THAM is currently selling an engineering package for $120. Company officials estimate that each time they reduce the price by $1, they will increase their sales.
# of $1 reductions: 10, 20, 30, 40, 50
Revenue: 7280, 9660, 10640, 10220 8400
2007-08-27 14:23:22 · 2 answers · asked by Physics 101 1 in Science & Mathematics ➔ Mathematics
feed prices, 110, 100, 90, etc., and revenue to your ti-83 or ti-84, plot the data, see the nice parabola, tell it to do a stat/calc/quadratic regression, get
y = -7p² + 1232p - 43540,
where y is revenue and p is price. and R² is exactly 1.
line of symmetry is p = -1232/(2*-7) = 88. so that's 32 $1 price reductions.
2007-08-27 14:51:34 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
See, all the points are on a parabola, therefore when you plot the parabola, the maximum value will be the ideal point of greatest revenue.
2007-08-27 14:29:52 · answer #2 · answered by way2hot2becool 3 · 0⤊ 0⤋