SOLUTION: Each year, a baseball team sells boxes of chocolates as a fundraiser to lower the cost of team fees. The price of the chocolates and the number of boxes sold varies each year. The
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Question 1189168: Each year, a baseball team sells boxes of chocolates as a fundraiser to lower the cost of team fees. The price of the chocolates and the number of boxes sold varies each year. The information from five years of sales are given in the table below.
Price per box ($) 3.00 4.00 5.50 6.50 8.00
Boxes sold 5837 3571 1950 1409 1118
a. Find the regression equation in the form 3 2 y ax bx cx d = + ++ that best approximates the
data. Express the values of a, b, c, and d to the nearest hundredth.
b. Use the equation to find the number of boxes, to the nearest whole number, that the team will sell if they charge $4.35 per box.
c. One year, the team only sold 366 boxes of chocolates. What price did they charge for each
box?
d. If the team raises the price too high, they will not sell any boxes. Use your regression equation to predict the price of a box that will result in zero boxes sold.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Part (a)
You will need a graphing calculator or other similar form of technology to determine the regression equation. It can be done by hand, but such a process is tedious busywork.
You should find the cubic regression equation is approximately
Answer:
a = -45.69
b = 1005.15
c = -7567.95
d = 20716.83
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Part (b)
Plug in x = 4.35 and simplify
Answer: 3055 boxes
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Part (c)
Plug in y = 366 and solve for x. You'll need a graphing calculator again.
Effectively, you are looking where the horizontal line y = 366 and the cubic curve intersect.
When using a graphing calculator, that location is approximately (9.5, 366)
Answer: $9.50 per box
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Part (d)
Like with part (c), we'll use a y value to determine x.
This time, we use y = 0 to find x.
Use the root finder feature on your calculator to determine that the x intercept is approximately (9.88, 0)
Answer: $9.88 per box
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