A College Bookstore has been selling one particular tee shirt for a year now. During the Fall term, 100 were sold at a price of $5 each. During the following Spring term, the price was raised to $7; consequently, only 80 were sold. 1. Suppose that the number of tee shirts sold (N) depends linearly on the price charged (x). Write an equation showing this dependence. Identify and explain the meaning of the slope and the vertical intercept. Then graph the function. 2. According to this relationship, how many tee-shirts would be sold during a term at $3.50 each? What should the cost of a shirt be in order to sell 45 of them in a term?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
In this task we will assume that the number of items sold (N) depends linearly on the price charged for that item (x). From this, you will show that the profit yield (P) depends on the price charged according to a quadratic rule.
A College Bookstore has been selling one particular tee shirt for a year now. During the Fall term, 100 were sold at a price of $5 each. During the following Spring term, the price was raised to $7; consequently, only 80 were sold.
1. Suppose that the number of tee shirts sold (N) depends linearly on the price charged (x). Write an equation showing this dependence. Identify and explain the meaning of the slope and the vertical intercept. Then graph the function.
2. According to this relationship, how many tee-shirts would be sold during a term at $3.50 each? What should the cost of a shirt be in order to sell 45 of them in a term?
3. Suppose that it costs the Bookstore $3 for each shirt.
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- Calculate the total profit during terms where they charge: $5, $6, $7, $8, $9, $10.
- Then calculate the average rate of change in total profit between charging: $5 & $6; $6 &$7; $7 & $8; $8 & $9; $9 & $10 and construct a rate of change table (see below).
- Use these data to explain why profit does not depend linearly on price.
- Extend the table (see below) appropriately and explain why profit, P(x) depends quadratically on price.
- Determine the parameters a, b and c in the quadratic model p(x)=ax2+bx+c
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