Question

III.

a small appliance manufacturer finds that if the firm produces and sells x blenders
monthly, the total monthly profit P (in dollars) is given by
P(x) = 8x + 0.3x2 - 0.0013x3 - 372.
ne owner wants to produce no more than 225 blenders/month in order to maintain quality
(SLO #1, 2, 6)
a. Find the y-intercept and explain what it means in this context.

Answer 1

• The y-intercept is - 372 and it means that if the manufacturers do not produce and sell any blenders they will have a loss of $ 372.

Step-by-step explanation:

The polynomial that represents the function is:

• 
  `P(x)=8x+0.3x^2-0.0013x^3-372`

Where the variable, x, represents the number of blenders produced and sold monthly, and P(x) is the monthly profit in dollars obtained for the sale of x blenders.

As for the question, the y-intercept is the point on the graph where the function crosses the y-axis, i.e. where the input of the function is x = 0.

Therefore, the y-intercept is the value of the function for x = 0, P(0), and it is found by substituting 0 for x in the polynomial function, which is shown next:

• 
  `P(0)=8(0)+0.3(0)^2-0.0013(0)^3-372=-372`

The meaning of this value is that the firm loses $372 when it does not produce and sell any blenders.