Answer:
The right answer is:
(A) [tex]40x-300.25[/tex]
(B) [tex]15[/tex]
(C) [tex]383[/tex]
Step-by-step explanation:
Given:
Producing x items,
= [tex]55x+300[/tex]
Revenue x items,
= [tex]95x-0.5^2[/tex]
= [tex]95 x-0.25[/tex]
Part A:
= [tex]R(x)-C(x)[/tex]
By putting the values, we get
= [tex](95x-0.25)-(55x-0.25)[/tex]
= [tex]40x-300.25[/tex]
Part B:
We know,
P(x) = $300
⇒ [tex]300=40x-300.25[/tex]
[tex]40x=600.25[/tex]
[tex]x=\frac{600.25}{40}[/tex]
[tex]=15.00625[/tex]
or,
[tex]=15[/tex]
Part C:
We know,
P(x) = $15,000
⇒ [tex]40x-300.25=15000[/tex]
[tex]40x=15300.25[/tex]
[tex]x=\frac{15300.25}{40}[/tex]
[tex]=382.50625[/tex]
or,
[tex]=383[/tex]
The values of x that create a profit of $300 is 60 or 20 items.
Profit is the difference between revenue and cost, it is given by:
Profit = revenue - cost
a) From the situation:
Profit (P) = 95x−0.5x² - (55x + 300)
P = -0.5x² + 40x - 300
B) For a profit of $300:
-0.5x² + 40x - 300 = 300
-0.5x² + 40x - 600 = 0
x = 60 and x = 20
c) For a profit of $15000:
-0.5x² + 40x - 300 = 15000
-0.5x² + 40x - 15300 = 0
The equation cannot be solved
The values of x that create a profit of $300 is 60 or 20 items.
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