Question

An ice cream shop uses the function f(p)=2.50p-300 to calculate the amount of profit or loss, f(p), the store makes each day after selling p number of ice cream cones which domain is appropriate for the function and shows the ice cream shop making a profit?

A. all positive integers
b. all positive rational numbers
c. all integers greater than 120
d. all rational numbers greater than 120

Answer 1

c. all integers greater than 120

Explanation:

For making profit, f(p) must be positive. You want f(p) to be greater than zero.

2.50p - 300 > 0

2.50p > 300

p > 120

Since the number of cones sold is always a whole number, the domain must be all integers greater than 120.

Answer: c. all integers greater than 120

Answer 2

p > 120. p is an integer. Answer C

Explanation:

If all you are interested in is profit, then you must find the break even point. The break even point is showing neither a profit nor a loss.

The break even point is the point where the function f(p) = 0. Be careful that you understand that p is not zero. The y value or f(p) is 0.

2.50p - 300 = 0 Add 300 to both sides

2.50p - 300 + 300 = 0 + 300 Combine

2.50p = 300 Divide both sides by 2.5

2.50/2.50 p = 300/2.50 Do the division

p = 120 cones

Conclusion

He must sell 120 cones to break even.

A: wrong. Any number less that 120 and he is not making money

B: wrong. What would it mean is p= 300.333 cones? What does the 0.333 stand for.

C: Correct. He has to sell an integer number of cones > 120

D: Wrong. Same reason as B