MATH SOLVE

2 months ago

Q:
# A company manufactures shampoo. The total monthly cost of manufacturing shampoo is equal to fixed cost of $400 plus a cost of $40 per gallon of shampoo manufactured. On the grid provided, plot 5 points and draw a line to show the relationship between the number of gallons of shampoo manufactured per month, x, and the total cost per month, y.

Accepted Solution

A:

I don't have the grid, so you'll have to actually plot the points and draw the line yourself. But I can help you calculate some points to plot.

Let's start off with 0 gallons of shampoo. So 0 times $40 = $0 and we have a fixed cost of $400. So the result is $0 + $400 = $400. And there's your first point (0, 400).

Now let's do 1 gallon of shampoo. 1 times $40 = $40 and we have to add the fixed cost of $400, so the result is $40 + $400 = $440. And your second point is (1,440).

In fact, we can create the function

c(x) = 40*x + 400

to express the cost for any amount of shampoo. So let's calculate 3 more points

c(2) = 40*x + 400 = 40 * 2 + 400 = 80 + 400 = 480

c(3) = 40*x + 400 = 40 * 3 + 400 = 120 + 400 = 520

c(4) = 40*x + 400 = 40 * 4 + 400 = 160 + 400 = 560

So 3 more points to plot are (2,480), (3,520), and (4,560).

And you've gotten your 5 points. They are (0,400), (1, 440), (2, 480), (3, 520), and (4, 560). Just plot them on your chart and draw a straight line through all 5 of them. And they will be in a straight line, if they're not, then you plotted them incorrectly.

Let's start off with 0 gallons of shampoo. So 0 times $40 = $0 and we have a fixed cost of $400. So the result is $0 + $400 = $400. And there's your first point (0, 400).

Now let's do 1 gallon of shampoo. 1 times $40 = $40 and we have to add the fixed cost of $400, so the result is $40 + $400 = $440. And your second point is (1,440).

In fact, we can create the function

c(x) = 40*x + 400

to express the cost for any amount of shampoo. So let's calculate 3 more points

c(2) = 40*x + 400 = 40 * 2 + 400 = 80 + 400 = 480

c(3) = 40*x + 400 = 40 * 3 + 400 = 120 + 400 = 520

c(4) = 40*x + 400 = 40 * 4 + 400 = 160 + 400 = 560

So 3 more points to plot are (2,480), (3,520), and (4,560).

And you've gotten your 5 points. They are (0,400), (1, 440), (2, 480), (3, 520), and (4, 560). Just plot them on your chart and draw a straight line through all 5 of them. And they will be in a straight line, if they're not, then you plotted them incorrectly.