After several weeks of mowing and edging yards in their neighborhood, Desmond and Shelly meet to reconsider the estimated times for mowing and edging standard sized interior and larger corner lots.

Question

After several weeks of mowing and edging yards in their neighborhood, Desmond and Shelly meet to reconsider the estimated times for mowing and edging standard sized interior and larger corner lots. Recall the original estimate they came up with:

Standard size interior lot: 1 hour to mow and 1/2 hour to edge

Larger corner lot: 2 hours to mow and 45 minutes to edge

Also, recall the system of inequalities that represents the constraints on the number of interior lots, x, and the number of a corner lot, y, that Desmond and Shelly can mow in one week: 

        

_< or >_ means equal or greater than

x + 2y _< 36

1/2x + 3/4y _< 15

x >_ 0

y >_ 0

Desmond is still satisfied that the mowing estimates are accurate. Shelly thinks the edging time for a standard lot is accurate, but she has determined that the edging time for a corner lot should be 1 hour, not 45 minutes.

a.   If Desmond continues to allocate a maximum of 36 mowing hours per week and Shelly continues to allocate a maximum of 15 edging hours per week, write the system of the inequalities that now represents the constraints on the number of interior lots, x, and the number of corner lots, y, that Desmond and Shelly can mow in one week.

b.  Sketch the feasible region that represents all solutions to this new system of inequalities. In other words, show all feasible weekly schedules for mowing and edging based on these new constraints.

c.   What is different about this system compared to the other systems you have considered? (hint: How does this graph look different than other inequality graphs we have seen?)

d.   what is the practical significance of this difference? What does this mean about the scheduling?

Answer 1