You own a business and need to answer the following questions:
1
1
You are told that the demand for a certain product can be described by the equation:
D = 4000 – 44C (for values of C between 10 and 90)
D is the demand, in pounds, for the product.
C is the cost per pound in cents.
In addition, the supply of this product from the distributor is described by the equation
S = -1340 + 134C (for values of C between 10 and 90)
S is the supply, in pounds, of the product.
C is the cost per pound in cents.
When the supply exceeds the demand, the price will go down. On the other hand, when the demand exceeds the supply, the price will go up. At what cost per pound will the price stabilize and the supply equal the demand?
2
1
You need to estimate the total cost for a job that requires a large volume of copying. After a phone call to the copy shop, you find that each copy on white paper costs $0.045. On colored paper, it costs $0.065. In addition, there is a $5 handling fee for jobs that exceed 500 copies. Each packet of materials that you will duplicate has 5 colored pages and 27 white pages.
a. Write a formula that can be used to determine the total cost for producing n packets, when n is greater than 500.
b. Suppose your supervisor tells you that this project has only $2000 allotted for copying costs. Use your formula to determine the number of packets you can produce with this allotted amount.
3
1
The “Rule of 72” is a way to estimate the effect of compound interest on an investment. The rule states that you divide the annual percentage interest rate (expressed as a percent not a decimal) into 72 to find the approximate number of years needed to double the value of your investment.
a. Write the “Rule of 72” as a formula. Be sure to identify the variables that you choose to use.
b. Use your formula to find out how long it would take to double a $500 deposit in an account that paid an annual interest rate of 8.5%.
c. Use your formula to find out what interest rate would be needed to double an investment in five years.
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