Questions: The number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked. 1) Find the constant of proportionality, k, to 2 decimal places if 610 workers work 20 hours and can produce 79178 widgets. k= 2) How many widgets (to the nearest tenth) can be produced by 655 workers in 37 hours? Widgets =

The constant of proportionality (k) is 6.49.

This solution assumes that the production of widgets is directly proportional to both the number of workers and the time they work, with a constant of proportionality that does not change for different numbers of workers or time periods. It also assumes a linear relationship without considering factors like diminishing returns or efficiency changes at different scales of operation.

Once the constant of proportionality (k) is known, the number of widgets that can be produced by any number of workers over any period can be predicted using the formula: $$ W = kNT $$ Substituting the known values, we get: $$ W = 6.5\times655\times37 = 157527.5 $$

The number of widgets that can be produced is 157527.5.

This solution assumes that the production of widgets is directly proportional to both the number of workers and the time they work, with a constant of proportionality that does not change for different numbers of workers or time periods. It also assumes a linear relationship without considering factors like diminishing returns or efficiency changes at different scales of operation.