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
= [tex]-\frac{160000}{1000} + \frac{7600}{10} - 350[/tex]
= - 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. ∴,
[tex]\frac{d}{dx} P(x) = \frac{d}{dx}(- 0.001x^{2} + 1.9x - 350)[/tex]
[tex]\frac{d}{dx}(- 0.001x^{2} + 1.9x - 350) = 0[/tex]
[tex]- 0.002 x + 1.9 = 0[/tex]
[tex]x = \frac{1.9}{0.002}[/tex]
[tex]x = 950[/tex]
Therefore, the Company should produce 950 donuts daily in order to maximize its profits.
