Acompany’s total cost from manufacturing and selling x units of their product is given by: y = 2x2 – 600x + 49,000. how many units should be manufactured in order to minimize cost, and what is the minimum cost? a. (100, $9,000)b. (125, $3,250)c. (150, $4,000)d. (170, $4,800)e. (200, $9,000) the cost of producing x hundred items is given by the equation c(x) = 2x2 – 4x + 4 and the revenue generated from sales of x hundred units is given by the equation r(x) = –4x2 + 74x – 176. what values of x will the company break even? a. 2 or 12b. 2 or 16c. 3 or 8d. 3 or 10e. 4 or 12 the profit from manufacturing and selling x units of a tablet pc is given by: p(x) = –.03x2 + 1,200x – 34,000how much profit should the company expect from selling 20,000 tablets? a. $36,000,000b. $24,000,000c. $23,966,000 d. $22,000,000 e. $11,966,000

a)   c ( 150,  $ 4,000)

b)   d ( 3 or 10 )  

c)  e  11,966,000 $

Step-by-step explanation:

a) C(t)  =  2x² - 600x + 49000

Taking derivatives on both sides of the equation

C´(t)  =  4x - 600          C´(t)  = 0        4x - 600 = 0        x =  150

And minimun cost is:

C(min) =   2x² - 600x + 49000  ⇒ C(min) = 2* ( 150)²  -  600* (150) +49000

C(min) = 4000 $

b) x hundred of tems cost

C(x)  =  2x² - 4x  + 4      and revenue generated is R(x) = -4x² +  74x -176

Then  C(x)  should be equal to  R(x)

2x² - 4x  + 4   =   -4x² +  74x -176

Solving for x  

6x² - 78x +  180  = 0       ⇒  x² - 13x + 30  =  0

x₁,₂  =  13 ± √( 169 - 120) /2        x₁  =  10        x₂  =  3

c)  Th profit for manufacturing and selling tablets

P(x)  - 0,03*x²  + 1200x  -  34000

where x is numbers of tablets. If the company sells 20000 tablets then

P(x)  = - 0,03* (20000)²  +  1200 (20000)  - 34000

P(x)  = - 0,03 * 4 *10⁸  +  24* 10⁶   - 34000

P(x)  =  - 12000000  +  24000000  - 34000

P(x)  = 11966000 $

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