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QuestionA plant makes 50 clubs for \4863and70clubsfor$6163.Findcostfunction4863 and 70 clubs for \$6163. Find cost function \mathrm{C}(x)andgraphitfor and graph it for 0 \leq x \leq 200$. Interpret slope and intercept.

Studdy Solution

STEP 1

Assumptions1. The plant can manufacture50 golf clubs per day at a total daily cost of 4863..Theplantcanmanufacture70golfclubsperdayatatotaldailycostof4863. . The plant can manufacture70 golf clubs per day at a total daily cost of 6163.
3. The daily cost and production are linearly related.
4. We need to find the total daily cost, C, of producing x golf clubs.

STEP 2

We will use the formula for the slope of a line to find the slope (m) of the cost-production line. The slope is given by the difference in the y-values divided by the difference in the x-values.
m=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Plug in the given values for the cost (y) and the number of golf clubs (x) to calculate the slope.
m=6163−486370−50m = \frac{6163 -4863}{70 -50}

STEP 4

Calculate the slope.
m=130020=65m = \frac{1300}{20} =65

STEP 5

Now that we have the slope, we can use the point-slope form of a line to find the equation for the cost-production line. The point-slope form is given byy−y1=m(x−x1)y - y1 = m(x - x1)

STEP 6

We can use either of the given points for (x1, y1). Let's use (50,4863). Plug in the values for the slope and the point to find the equation for the line.
y−4863=65(x−50)y -4863 =65(x -50)

STEP 7

implify the equation to find the cost-production line.
y=65x−65⋅50+4863y =65x -65 \cdot50 +4863

STEP 8

Calculate the y-intercept.
y=65x−3250+4863=65x+1613y =65x -3250 +4863 =65x +1613So, the total daily cost, C, of producing x golf clubs is given byC=65x+1613C =65x +1613

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