Question #7

This assignment uses least squares regression to find the total cost function for a manufacturing process. This equation will then be used with revenue information to determine the processs break-even point.

Gizmo Game Co. has developed a new process to manufacture its latest childrens game, which they customize for each order. So far, Gizmo has produced 17 batches of games to meet 17 different orders. The batch size of each order and the total cost of producing the batch are shown in the table below.

1. Make a scatter (XY) chart of Total Cost (Y) vs. Batch Size (X).	Batch Size (# games)	Total Cost
	20	$1,245
2. Find the least squares regression equation that gives Total Cost as a	35	$1,640
linear function of the number of games produced in a batch.	20	$1,500
The least squares regression equation here is:	45	$1,600
	40	$1,950
Y=20.098x+816.33	25	$1,000
	70	$2,425
3. Accurately plot the regression line on your scatterplot either by hand	50	$2,100
(carefully) or by using the Excels Add Trendline tool.	15	$820
	60	$2,025
	80	$2,200
4. Based on the regression equation, what is the:	55	$2,100
4a) fixed cost of producing a batch? 816.33	95	$2,625
4b) variable cost of producing a game? 20.1 5. The strength of the linear relationship between Total Cost and Batch Size is weak, moderate or, strong Strong because	60	$2,165
	70	$2,000
	50	$1,450
	100	$2,920
(support your answer with a number) _____0.8335 R Square________________.

6. Suppose that Gizmo sells each game for $33.95. Assuming your regression equation above accurately

reflects their total costs, calculate the:

6a) BEP_x = Break-even point in games:

58.9322

6b) BEP_$ = Break-even point in dollars:

2000.81

7. Gizmo receives an order 85 games which they plan to make in one batch. What is the expected:

7a) Total cost of this batch?

7b) Total profit from this batch?