Question

The number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked. find the constant of proportionality k to 2 decimal places if 735 workers work 17 hours and can produce 74345.25 widgets.

Answer 1

To find the constant of proportionality k for a manufacturing plant where workers' production varies jointly with the number of workers and hours worked, substitute the given values into the joint variation formula and solve for k. In this instance, k is approximately 6.21.

Step-by-step explanation:

The number of widgets that a manufacturing plant produces is said to vary jointly as the number of workers and the time they have worked. To find the constant of proportionality, k, we set up the following equation based on the joint variation model:

Widgets = k × (Workers) × (Hours)

In this problem, we have:

• Widgets = 74345.25
• Workers = 735
• Hours = 17

Substitute the given values into the model to solve for k:

74345.25 = k × 735 × 17

To find k, divide both sides of the equation by the product of the workers and hours:

k = 74345.25 / (735 × 17)

k ≈ 6.21

Therefore, the constant of proportionality k is approximately 6.21.