The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below. Price 0.00 0.45 0.60 0.75 1.00 1.25 1.40 1.50 Profit 0.00 $720 $900 $990 $845 $625 $560 $300 What factors might influence how much is to be made from the candy sale? Give at least two. What happens to the profit as the price of each candy bar increases? Explain possible reasons for your observations. How do you suppose the other bands determined the price at which to sell each candy bar?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below.
|
Price |
0.00 |
0.45 |
0.60 |
0.75 |
1.00 |
1.25 |
1.40 |
1.50 |
|
Profit |
0.00 |
$720 |
$900 |
$990 |
$845 |
$625 |
$560 |
$300 |
- What factors might influence how much is to be made from the candy sale? Give at least
two.
- What happens to the profit as the price of each candy bar increases?
Explain possible reasons for your observations.
- How do you suppose the other bands determined the price at which to sell each candy bar?
- Do any data values seem unusual? Yes or No (circle one)
Why?
- Which quantities do the independent and dependent variables represent?
Independent variable:
Dependent variable:
- Draw the
scatterplot of the data. Sketch the graph below. Label both axes with what each
represents as well as a numerical scale.
- Does the relationship look linear or quadratic?
- Using your graphing calculator, find the model (equation) that represents the
line or curve of best fit. Write it here.
9. Accurately draw the curve on the graph of the scatterplot that you drew for #6. Find the vertex and intercepts of your model.
10. Does the curve look like a good model? Circle one: Yes or No
11. Predict the profit if they charge $1.75 for each candy bar. Is this interpolation or extrapolation? Does it make sense? Show work.
Profit: ____________________
Circle one: Extrapolation or Interpolation
Does this prediction make sense? Yes or No
Why or Why not?
- Predict the profit if they charge $1.15 for each candy bar. Is this interpolation or extrapolation? Show work.
Profit: ____________________
Circle one: Extrapolation or Interpolation
- Find the price the band should charge to obtain the maximum profit. What is the profit? Think about where the maximum occurs for a quadratic function. Show work.
Price: ____________________
Profit: ____________________
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