The area of a parking lot is 805 square meters. A car requires 5 square meters and a bus requires 32 square meters of space. There can be at most 80 vehicles parked at one time. If the cost to park a car is $2.00 and a bus is $6.00, how many buses should be in the lot to maximize income?

Please no direct answers.

Question

The area of a parking lot is 805 square meters.  A car requires 5 square meters and a bus requires 32 square meters of space.  There can be at most 80 vehicles parked at one time.  If the cost to park a car is $2.00 and a bus is $6.00, how many buses should be in the lot to maximize income?

Please no direct answers.

haleyelizabeth2017 · Answer

Would the first inequality be $$5c+32b \le 805$$?

hero · Answer

looks right

haleyelizabeth2017 · Answer

Okay...I'm not sure what to put for the second one...$c+b\le 80$?

hero · Answer

why did you write 805 Instead of 80 ?

haleyelizabeth2017 · Answer

there are 805 square meters in the parking lot.

haleyelizabeth2017 · Answer

Shoot...typo, sorry.

hero · Answer

Wait. Yoo mean 85

haleyelizabeth2017 · Answer

I made a typo...I meant 805, my bad

hero · Answer

Assuming your inequalities are correct, what do you think would be the next step?

haleyelizabeth2017 · Answer

Don't I need a third inequality?  For prices?

haleyelizabeth2017 · Answer

oh wait...no...I use the prices to find the min/max!  So f(x,y)=2c+6b?

hero · Answer

Correct

haleyelizabeth2017 · Answer

Will there only be one intersection point then?

haleyelizabeth2017 · Answer

But, would max be at (65,15) so 15 buses?

hero · Answer

There's a range of points Within a region that are possible, but there is only one correct pair of coordinates that will maximize the profit

hero · Answer

Show we how you found that result.

haleyelizabeth2017 · Answer

I have no idea...I just chose the intersection point...I'm sorry, I'm having a hard time understanding these word problems...with only two inequalities to graph...

hero · Answer

There's almost always four inequalities to graph and you usually use x and y for variables

haleyelizabeth2017 · Answer

When I dealt with the three inequalities I plugged in the intersection points into the f(x,y) function...

hero · Answer

Because you also consider .$$c \ge 0$$ and $$b \ge 0$$

haleyelizabeth2017 · Answer

oh.

hero · Answer

but If you use x and y as variables, then you can use a platform like desmos to plot your inequalities

haleyelizabeth2017 · Answer

That's what I'm doing :)

haleyelizabeth2017 · Answer

So, the intersection points I have now are:
(80, 0)
(65, 15)
(0, 25.16)
(0,0) 

But we can tell already that (0,0) will not be the maximum.

haleyelizabeth2017 · Answer

It is (65,15).

haleyelizabeth2017 · Answer

f(80,0)=160
f(0, 25.16)=150.96
f(0,0)=0
f(65,15)=220

haleyelizabeth2017 · Answer

Would you mind helping me with a couple more?

hero · Answer

Sure, but you seem to already know what you are doing for the Most part.

haleyelizabeth2017 · Answer

I think for one I just need it checked...not sure about the last one..

haleyelizabeth2017 · Answer

Eh I'll just post the one I need help on :)