Stores such as Sam's Club and Costco charge an annual membership fee of approximately $55. As a member you can purchase products at lower prices, but typically in larger quantities than one buys at ordinary stores. Savings vary from product to product, but for this question, let us assume you can save $20 for every $100 dollars you spend at one of these stores compared to shopping elsewhere.

a. Suppose you spend $100 dollars in one year at such a store. Do you come out ahead? How much do you save (or lose?) compared to not having membership and paying full price?
b. Create a table in Excel showing the amount you spend in the first column with the corresponding overall savings in the second column. In the spend column, start with zero dollars and go up to $600 in increments of $100.
c. How much do you have to spend at the store for it to be worthwhile for you to buy a membership?
d. The amount you save (or lose) by buying membership is a linear function of how much you spend. Explain why.
e. What are the two variables in this function? Assign each variable a letter. Write the linear equation for your savings as a function of how much you spend at the store.
f. From the analysis above, one of the factors one should consider when deciding whether or not to join a store such Sam's Club or Costco is whether or not you are going to spend a certain minimal amount at the store in a year. What other factors should you consider when deciding whether to become a member of Sam's Club or Costco?