Question

The below table includes the number of X-Rays taken and X-Ray costs over the last nine months at VG Hospital. X-Rays Taken X-Ray Costs Jan 6,250 $28,000 Feb 7,150 $33,500 Mar 5,000 $23,000 Apr 4,250 $20,000 May 4,500 $22,000 Jun 3,000 $18,310 Jul 3,500 $19,000 Aug 5,500 $24,000 Sep 5,750 $26,000 (round your answers to nearest dollar for “a” and two decimal places for “b” in your Y = a + bX formula)

a)  Calculate the "b" (Variable Cost component, the slope of the line) for the Y = a + bX cost function for X-Ray costs (to two decimal places)

b) Using your cost function, predict what the X-Ray costs would be in October if you expect 5150 X-Rays
(enter response to the nearest dollar)

Answer 1

	X-Rays taken	X-Ray costs
Highest activity	7,150	$33,500
Lowest activity	3,000	$18,310

a)

Variable cost per X-Rays taken = (Highest activity cost - Lowest activity cost)/(Highest activity - Lowest activity)

= (33,500 - 18,310)/(7,150 - 3,000)

= 15,190/4,150

= $3.66

Fixed cost = Highest activity cost - (Highest activity x Variable cost per X-Rays taken)

= 33,500 - (7,150 x 3.66)

= 33,500 - 26,169

= $7,331

b)

X-Ray costs in October for 5150 X-Rays taken

Total cost = a + bX

= 7,331 + 3.66 x 5,150

= 7,331 + 18,849

= $26,180