A company is manufacturing two different models of lamps, a table lamp and a floor lamp.

Question

A company is manufacturing two different models of lamps, a table lamp and a floor lamp. A table lamp takes 1 hour to make and a floor lamp takes 2 hours to make. The company has 9 employees working 8-hour days. The total manufacturing capacity is 40 lamps per day.

Let x = table lamp and y = floor lamp. Write the inequality for the number of lamps in standard form.

Answer 1

There can only be 40 total lamps so the total number of x lamps plus y lamps is, at most 40.

Which gets us to here:

x + y <=40

Also, there cannot be a negative amount of lamps created which gets us:

x >= 0

y >= 0

However, as you'll notice from the question, the 9 employees work just 8 hours per day each, for 9 * 8 = 72 hours worked daily. If x was 0 and y was 40, well then, we'd have 40 lamps * 2 hours to produce each = 80 hours of work which makes it impossible for y to be 40. The maximum 7 can be is:

72 hours worked / 2 hours per floor lamp = 36 total floor lamps possible (y lamps)

Therefore, we end up with:

y + x <= 40 | The total numbers of lamps is between 0 and the maximum capacity of 40 each day.

0 <= x <= 40 | The total of x lamps is either 0 or up to 40, the maximum capacity.

0 <= y <= 36 | The total of y lamps is either 0 or up to 36, the maximum capacity factoring in hours worked.

Answer 2

x + y ≤ 40

What role do the 9 employess play?