Math 142
Section 1.2 Examples
Example 1: Suppose we are opening a cat adoption clinic. For each month, the cost of care for
a cat is $60. For all other costs, we pay $750 for the month. Assuming the cost is linear, write a
formula for the cost of the cat clinic for one month.
Example 2: A sandwich shop owner is calculating her weekly cost. When she makes 30 sandwiches
in a week, her cost is $140. When she makes 50 sandwiches in a week, her costs jump to $200.
Assuming the cost is linear, write the cost function for the week.
Math 142
Section 1.2 Examples
Example 3: In the sandwich shop above, the owner sells each sandwich for $6. Assuming the
revenue is linear, what is the revenue function? What is the profit function for the sandwich shop?
Example 4: How many sandwiches must the owner sell in order to break even?
Math 142
Section 1.2 Examples
Example 5: In our cat clinic, when we adopt out 33 cats our revenue is $2790. Assuming the
revenue is linear, how many cats must we adopt out to break even?
Example 6: Suppose the quantity demanded of an alarm clock is 48,000 when it costs $8. When
it costs $12, demand drops to 32,000 alarm clocks. Find the price-demand equation, assuming it’s
linear. How much are the clocks going for if demand is 40,000 units? How many will be demanded
if they cost $14?
Math 142
Section 1.2 Examples
Example 7: A supplier of the alarm clocks will not manufacture them if the price is less than $17.
The supplier will make 75,000 alarm clocks if the price is $24.50. Find the price-supply equation,
assuming it is linear. Given the demand from the previous example, what is the equilibrium
quantity? What is the equilibrium price?
Example 8: The demand equation for cat food 3x + 5p = 15, where p is the price and x is the
number of thousands of cat toys. What is the revenue equation for the cat toy manufacturer?
Example 9: How many cat toys should be manufactured in example 8 to maximize revenue? How
much should we charge?