A study was conducted to investigate the relationship between the cost, y (in tens of thousands of dollars), per unit of equipment manufactured and the number of units produced per run, x. The resulting equation for the line of best fit is given below, with x being observed for values between 10 and 200.
y = 7.13 − 0.01x
(a) If a production run was scheduled to produce 55 units, what would you predict the cost per unit to be in tens of thousands of dollars? $(00,000)
(b) What would be the cost per unit in dollars? $
Substitute 55 for x, then solve the equation for y.
To answer the question, we need to substitute the value of 55 for x in the equation y = 7.13 - 0.01x.
(a) The equation y = 7.13 - 0.01x is in terms of tens of thousands of dollars. To find the cost per unit in tens of thousands of dollars, we substitute x = 55 into the equation:
y = 7.13 - 0.01(55)
y = 7.13 - 0.55
y = 6.58
Therefore, the predicted cost per unit in tens of thousands of dollars would be 6.58.
(b) To find the cost per unit in dollars, we need to multiply the predicted cost per unit in tens of thousands of dollars by 10,000:
6.58 * 10,000 = 65,800
Therefore, the predicted cost per unit would be $65,800 in dollars.