Question

The profit from the sale of x units is P(x)=80x−1200−x^2

a) How many units do they need to sell in order to break even? Enter your answers separated by a comma.

   

b) What production level maximizes profit, and what is the profit?

Production level =  

Profit = $

Answer 1

2 P(x) = 80% -1200 - To achieve Break Even points, profit= o te Tofal Revenue = Total costs so Pla=0 → 807-1200-720 102 - 80x+1200-0 2 -60% - 20% +1200-0 3 217-60) -2017-60)-0 |x=20] [2= 60 no Hence of 여 Unit they need Å sell in order to achieve Break Even point be 2= 20 x=60 2 To maxinures profits be P(x) = 80%-1200-2 d P1x) = ( 80% – 1200-~?) Jx dplx)= 80 - 22 du dre CA d p(x) = 0 an 80-29 = 0 alx=40

30 production level = 40 know 40 is the maximizes profits achieve , u TO we Gel from equi dp(x) = 80-21 da 7 d?p(x) = -2 a az E-ve = maximum Cese if double derivativen Negative profit be p(a)= 80-1200 -- 4+2 = 40, plX) 80140) - 1200-14032 2 =400 Hence (pro fith = $400