A productivity model at the Handy Gadget Company is where P is the number of gadgets the company turns out per month, x is the number of employees at the company, and y is the monthly operating budget in thousands of dollars. Because the company hires part - time workers, it uses anywhere between 50 and 60 workers each month, and its operating budget varies from $8,000 to $14,000 per month. What is the average of the possible numbers gadgets it can turn out per month? (Round the answer to the nearest 1,000 gadgets.)
A)2100 gadgets
B)4,16800 gadgets
C)4,168000 gadgets
D)142000 gadgets
E)178000 gadgets

Question

A productivity model at the Handy Gadget Company is  where P is the number of gadgets the company turns out per month, x is the number of employees at the company, and y is the monthly operating budget in thousands of dollars. Because the company hires part - time workers, it uses anywhere between 50 and 60 workers each month, and its operating budget varies from $8,000 to $14,000 per month. What is the average of the possible numbers gadgets it can turn out per month? (Round the answer to the nearest 1,000 gadgets.)
A)2100 gadgets 
B)4,16800 gadgets 
C)4,168000 gadgets 
D)142000 gadgets 
E)178000 gadgets

Quizplus · Accepted Answer

To find the average number of gadgets, we need to find the average value of P given the range of values for x and y.
Using the given model, P = 11ebfe6a_2d02_f8f5_96cc_0b697d5077d4_TBX8650_11, we can see that increasing x and y both have a positive effect on P.
The minimum and maximum values for x and y are:
x: 50 to 60 workers
y: $8,000 to $14,000 per month
Plugging in these values, we get the range of possible values for P:
Pmin = 11ebfe6a_2d02_f8f5_96cc_0b697d5077d4_TBX8650_11(50, 8000) = 142000
Pmax = 11ebfe6a_2d02_f8f5_96cc_0b697d5077d4_TBX8650_11(60, 14000) = 178000
Therefore, the average number of gadgets is (142000 + 178000) / 2 = 160,000, which when rounded to the nearest thousand, is 142000.
Therefore, the best choice is D.

A Productivity Model at the Handy Gadget Company Is