Answer:
At the average rate of making profit, it will take slightly more than 30 hours for the business to reach a profit goal of $500. (30.075)
Step-by-step explanation:
a) It is not clear what linear equation is desired. We are given enough information to write an equation relating the number of bracelets produced by each worker to the time it takes.
Let n represent the number of bracelets Danica produces. Let r represent the number of bracelets Darrelle produces. Let h represent time in hours.
.. r/3 = h/4 ... Darrelle produces 3 bracelets in 4 hours
.. 4r - 3h = 0 ... equation in standard form
.. r = (3/4)h ... equation in slope-intercept form (the intercept is 0)
.. n/5 = h/2 ... Danica produces 5 bracelets in 2 hours
.. 2n - 5h = 0 ... equation in standard form
.. n = (5/2)h ... equation in slope-intercept form
b) We have no idea what special functions were discussed in the course. Of course these equations can be graphed. (2-dimensional equations are easily graphed.)
c) A profit function can be written in terms of the number of bracelets produced. Then it can be solved to find when (h=?) profit is equal to $500.
.. Let p represent the total profit from production of bracelets.
.. p = 10.50*r + 3.50*n ... profit in terms of bracelets produced
.. p = 10.50*((3/4)h) + 3.50*((5/2)h) ... profit in terms of hours, where both work the same hours
.. p = 16.625 h
.. 500 = 16.625 h ... we want to find hours until $500 profit
.. 500/16.625 = h ≈ 30.0752
At the average rate of making profit, it will take slightly more than 30 hours for the business to reach a profit goal of $500.
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If you work out the timing of when bracelets are finished, assuming they are made at a constant rate, you find that there will be 23 of Darrelle's bracelets and 76 of Danica's bracelets finished in 30 hours and 40 minutes. These will yield a profit of $507.50. After another 8 minutes, Danica will have finished bracelet 77 to add another $3.50 to the profit total.
