A company operates two plants which manufacture the same item and whose total cost functions are and C₁ = 8.5 + 0.03 q₁² and C₂ = 5.2 + 0.04 q₂², where q₁ and q₂ are the quantities produced by each plant. The company is a monopoly. The total quantity demanded, q = q₁ + q₂, is related to the price, p, by p = 60 - 0.04 q. How much should each plant produce in order to maximize the company's profit?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

45.36 feet per second

step-by-step explanation:

tyrone travels 30 miles in 58.2 minutes.  

1 mile = 5280 feet; this means he travels

30(5280) = 158400 feet in 58.2 minutes.

1 minute = 60 seconds; this means he travels 158400 feet in

58.2(60) = 3492 seconds.

this gives us the unit rate of

158400/3492 = 45.36 feet per second.