Question

29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in

Answer 1

Answer:

(a) When 400 donuts are made daily the company's profits is 250 dollars.

(b)  The Company should produce 950 donuts daily in order to maximize its profits.

Step-by-step explanation:

Profit function P(x) = - 0.001 x² + 1.9x - 350

where p is the profit and x is the quantity of donuts made daily.

(a) If x = 400, the company's profit is:

P(x) = - 0.001 x² + 1.9x - 350

= - 0.001 (400)² + 1.9(400) - 350

= $-\frac{160000}{1000} + \frac{7600}{10} - 350$

= - 160 + 760 - 350

= 760 - 510

= 250

(b) The profit of a firm is maximum when MR = MC or MR - MC = 0 which is also known as break even point. In other words, at break-even point the profit function equals to zero. ∴,

$\frac{d}{dx} P(x) = \frac{d}{dx}(- 0.001x^{2} + 1.9x - 350)$

$\frac{d}{dx}(- 0.001x^{2} + 1.9x - 350) = 0$

$- 0.002 x + 1.9 = 0$

$x = \frac{1.9}{0.002}$

$x = 950$

Therefore, the Company should produce 950 donuts daily in order to maximize its profits.