a) The total monthly cost is the sum of the fixed cost and the variable cost. If q represents the number of cones sold in a month, the monthly cost c(q) is given by
c(q) = 300 + 0.25q
b) If q cones are sold for $1.25 each, the revenue is given by
r(q) = 1.25q
c) Profit is the difference between revenue and cost.
p(q) = r(q) - c(q)
p(q) = 1.00q - 300 . . . . . . slope-intercept form
d) The equation in part (c) is already in slope-intercept form.
q - p = 300 . . . . . . . . . . . . standard form
The slope is the profit contribution from the sale of one cone ($1 per cone).
The intercept is the profit (loss) that results if no cones are sold.
e) With a suitable graphing program either form of the equation can be graphed simply by entering it into the program.
Slope-intercept form. Plot the intercept (-300) and draw a line with the appropriate slope (1).
Standard form. It is convenient to actually or virtually convert the equation to intercept form and draw a line through the points (0, -300) and (300, 0) where q is on the horizontal axis.
f) Of the three equations created, we presume the one of interest is the profit equation. Its domain is all non-negative values of q. Its range is all values of p that are -300 or more.
g) The x-intercept identified in part (e) is (300, 0). You need to sell 300 cones to break even.
h) Profit numbers are
425 cones: $125 profit
550 cones: $250 profit
700 cones: $400 profit
Probability=(number of specific outcomes)/(total number of possible outcomes)
P(!Z)=25/26 as a fraction exact
P(!Z)≈96.2% (approximation to nearest tenth of a percent)
