A company'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 $