The monthly output p of a light bulb factory is given by the formula p = 450lk, where l is the amount invested in labor and k the amount invested in equipment (in thousands of dollars). if the company needs to produce 4,000 units per month, how should the investment be divided among labor and equipment to minimize the cost of production? the cost of production is l + k. (round your answers to the nearest cent.)investment in labor $investment in equipment $

C(p)  = 4,96 (in thousands of dollars)

l = 2980 $  invest in labor

k = 2980 $ invest in equipment

Step-by-step explanation:

Information we have:

Monthly output   P = 450*l*k       ⇒  k = P/450*l

But the production need to be 4000

Then k = 4000/450*l

Cost of production = l * k     (in thousands of dollars)

C(l)  =  l  + 4000/450*l

Taking derivatives (both members of the equation)

C´(l) = 1 - 400 /45*l²          ⇒ C´(l) = 0          ⇒ 1 - 400/45l²  = 0

45*l² -  400  = 0              ⇒  l²  = 400/45

l = 2.98 (in thousands of dollars)

l = 2980 $ And

k = 400/45*l           ⇒  k 400/45*2.98

k = 2.98  (in thousands of dollars)

C(p) = l + k

C(p)  =  2980 + 2980  

C(p)  = 5960 $

question

what is the value of the third quartile of the data set represented by this box plot? a. 19 b. 21 c. 26 d. 29

answer

c

the answer to the expression is 83