A plant can manufacture 50 golf clubs per day at a total daily cost of $5367 and 80 golf clubs per day for a total cost of $7617.
(A) Assuming that daily cost and production are lineraly related, find the total daily cost, C, of producing x golf clubs.
(b) Interpret the slope and y intercept of the cost equation.
a. The fixed cost and cost per club sum to the y intercept. The slope is the ratio of the two costs.
b. The y intercept is the fixed cost and the slope is the cost per club.
c. The y intercept is the cost per club and the slope is the fixed cost.

Question

A plant can manufacture 50 golf clubs per day at a total daily cost of $5367 and 80 golf clubs per day for a total cost of $7617.
(A) Assuming that daily cost and production are lineraly related, find the total daily cost, C, of producing x golf clubs.
(b) Interpret the slope and y intercept of the cost equation.
          a. The fixed cost and cost per club sum to the y intercept. The slope is the ratio of the two costs.
         b. The y intercept is the fixed cost and the slope is the cost per club.
          c. The y intercept is the cost per club and the slope is the fixed cost.

whpalmer4 · Answer

Think of the number of golf clubs as the x value, and the cost as the y value.  You've got two known points, (50, 5367) and (80, 7617).  Plot the points and draw a line through them.  Use the two points to determine the slope of the line with the formula $$m=\frac{y_2-y_1}{x_2-x_1}$$.  Use the point-slope formula $y-y_0 = m(x-x_0)$ to find the equation of the line with slope m passing through one of those points, then rearrange it into slope-intercept form $$y=mx+b$$to determine the y-intercept.  Now plug in x = 0 to find the overhead cost.