Manny Motors, Inc., can hire auto workers for $20 per hour, whereas robot arms cost $12 per hour to operate. The horizontal (labor) intercept of the isocost line is 3 million and the vertical (robot) intercept isocost line is 5 million. If Manny Motors' operating budget became $120 million, the vertical intercept would become
A) 6 million labor hours
B) 20 million labor hours
C) 10 million robot hours
D) 20 million robot hours
E) $120 million

Question

Quizplus · Accepted Answer

To find the vertical intercept of the isocost line, we need to solve for the number of robot hours that can be purchased with the operating budget.

Let L be the number of labor hours and R be the number of robot hours. 
Then, the equation for the isocost line is:

20L + 12R = operating budget

Using the given horizontal intercept, we can plug in L = 3 million and solve for R:

20(3 million) + 12R = operating budget 
60 million + 12R = operating budget 
12R = operating budget - 60 million 
R = (operating budget - 60 million) / 12

If the operating budget is $120 million, then:

R = (120 million - 60 million) / 12 
R = 5 million

Therefore, the vertical intercept is 5 million robot hours, which is choice C.