Question 1147822
let x equal the number of candles in each shipment.
if you use straight line equation, then the total cost is equal to y in the following equation:
y = mx + b
x is the number of candles in the shipment.
m is the average change in the cost per candle.
b is the fixed cost, regardless of the number of candles shipped.
you have two (x,y) coordinate points from which to calculate m.
they are (4,35) and (12,95).
the total cost is 35 when 4 candles are shipped.
the total cost if 95 when 12 candles are shipped.
you use these two points to find m.
m = (y2 - y1) / (x2 - x1)
let (x1,y1) = (4,35).
let (x2,y2) = (12,95).
m = (y2 - y1) / (x2 - x1) = (95 - 35) / (12 - 4) = 60/8.
formula becomes y = 60/8 * x + b
to find b, use either point and replace x and y with the values from that point.
i used (4,35).
formula becomes 35 = 60/8 * 4 + b
solve for b to get b = 35 - 60/8 * 4 = 280/8 - 240/8 = (280-240)/8 = 40/8.
formula becomes y = 60/8 * x + 40/8.
when x = 4, formula becomes y = 60/8 * 4 + 40/8 = 35.
when x = 12, formula becomes y = 60/8 * 12 + 40/8 = 95.
formula looks good.
your solution is that the formula to model the cost for x candles is:
y = 60/8 * x + 40/8.
this formula can be graphed as shown below:
<img src = "http://theo.x10hosting.com/2019/102901.jpg" alt="$$$" >
the fixed cost for shipping is 5 dollars.
that's the cost regardless of the number of candles that are shipped.
the variable cost is equal to 60/8 times the number of candles shipped.
when 4 candles are shipped, the fixed cost is 5 and the variable cost is 60/8 * 4 = 240/8 = 30 for a total cost of 5 + 30 = 35.
when 12 candles are shipped, the fixed cost is 5 and the variable cost is 60/8 * 12 = 720/8 = 90 for a total cost of 5 + 90 = 95.
the fixed cost is the cost when no candles are shipped.
per the formula this becomes 60/8 * 0 + 5 = 5.
note that y = 60/8 * x + 40/8 is the same equation as y = 7.5 * x + 5.
the graph of each of those two equations is the same red line.
the variable cost means the same as the incremental cost.
it's the cost for each additional unit sold.