Problem 3-1 (LO2 CC10, 11) (30 minutes) 1. a) Change in cost: Monthly operating costs at 90% occupancy (high level of activity):
450 beds × 90% = 405 beds;
405 beds × 30 days × $29 per bed-day | $352,350 | Monthly operating costs at 60% occupancy (low level, given) | 326,700 | Change in cost | $ 25,650 |

Change in activity: | | 90% occupancy (450 beds × 90% × 30 days) | 12,150 | 60% occupancy (450 beds × 60% × 30 days) | 8,100 | Change in activity | 4,050 |

| b) | Monthly operating costs at 90% occupancy (above) | $352,350 | | | Less variable costs
405 beds × 30 days × $6.333 per bed-day | 76,950 | | | Fixed operating costs per month | $275,400 |

2. | 450 beds × 70% = 315 beds occupied. | | | Fixed costs | $275,400 | | Variable costs: 315 beds × 30 days × $6.333 per bed-day | 59,850 | | Total expected costs | $335,250 |

Problem 3-2 (LO2 CC12, 13) (45 minutes) 1. The scattergraph is presented below.

X
X
Y
Y

Problem 3-2 (continued) 2. (Note: Students’ answers will vary, depending on how they draw their regression line.)

The fixed cost element can be obtained by noting the point where the regression line intersects the vertical (cost) axis. As shown on the scattergraph, this point is at approximately $2,500 per month. Given this figure, the variable cost element can be obtained by the following computation:

Total cost at 10,000 kilometres driven per month [approximate amount] | $16,110 | Total cost at 5,000 kilometres driven per month [approximate amount] | $13,730 | Change in cost | $ 2,380 | Variable cost per kilometre [$2,380 ÷ 5,000 kilometre] | $ 0.476 | Fixed cost (where the regression line intersects the Y axis) | $11,300 |

Therefore, the cost of operating the autos can be expressed as $11,300 per month plus $0.476 per kilometre driven or
Y =