Ally loves the beach and decides to spend the summer selling various ice cream products on the beach. From her account course, she knows that her total cost is calculated as
Total Cost= Fixed Cost + Various Cost
She estimates that her fixed cost for the summer season is $50 per day. She also knows that each ice cream product costs her $0.75 from her distributor.
a. Write the relationship for the daily cost y in terms of the number of ice cream products sold per day x.
b. What does the y-intercept represent in the context of this problem?
c. What is her cost if she sells 450 ice cream products?
d.What is the slope of the line?
e. What does the slope of the line represent in the context of this problem?
a. The relationship for the daily cost y in terms of the number of ice cream products sold per day x can be written as:
y = 50 + 0.75x
b. In this context, the y-intercept represents the fixed cost, which is the cost Ally incurs even if she does not sell any ice cream products. It means that regardless of the number of ice cream products sold, Ally will always have a cost of $50 per day.
c. To find her cost if she sells 450 ice cream products, we substitute x = 450 into the equation:
y = 50 + 0.75(450)
y = 50 + 337.50
y = 387.50
So her cost would be $387.50 if she sells 450 ice cream products.
d. The slope of the line is the coefficient of x, which is 0.75 in this case.
e. In the context of this problem, the slope of the line represents the additional cost Ally incurs for each ice cream product she sells. It indicates the rate at which the cost increases with each unit sold. In this case, for every additional ice cream product sold, Ally incurs an additional cost of $0.75.