3)The owner of a small-appliance manufacturer finds that if the firm produces and sells x blenders monthly, the total monthly profit P (in dollars) is given by P(x)=8x+0.3x2-0.0013x3-372. The owner wants to produce no more than 225 blenders/month in order to maintain quality.a)Find the y-intercept and explain what it means in this context.  b)Find the x-intercept(s) and explain what they mean in this context.  c)Determine the domain of the function in the context of this problem.  d)How many blenders per month should the company produce in order to have a monthly profit of at least $3000.  e)How many blenders should be produced in order to maximize profit? What would the annual profit be, rounded to the nearest dollar, if that many were produced and sold?

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Asked Dec 2, 2019
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3)The owner of a small-appliance manufacturer finds that if the firm produces and sells x blenders monthly, the total monthly profit P (in dollars) is given by P(x)=8x+0.3x2-0.0013x3-372. The owner wants to produce no more than 225 blenders/month in order to maintain quality.

a)Find the y-intercept and explain what it means in this context.

 

 

b)Find the x-intercept(s) and explain what they mean in this context.

 

 

c)Determine the domain of the function in the context of this problem.

 

 

d)How many blenders per month should the company produce in order to have a monthly profit of at least $3000.

 

 

e)How many blenders should be produced in order to maximize profit? What would the annual profit be, rounded to the nearest dollar, if that many were produced and sold?

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Expert Answer

Step 1

Hey, since there are multiple sub-parts posted, we will answer first 3 sub-parts. If you want any specific question to be answered then please submit that sub-part only or specify the sub-part number in your message.

a)Find the y-intercept and explain what it means in this context.
Given total monthly profit function is,

p(x) 8x+0.3x2-0.0013x3 -372
Substitute 0 for x to find the y-intercept
p (0)=8(0)+0.3(0)-0.0013(0) -372
=-372
Thus, y-intercept is 372.
For, no production, the owner had a loss of 372
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p(x) 8x+0.3x2-0.0013x3 -372 Substitute 0 for x to find the y-intercept p (0)=8(0)+0.3(0)-0.0013(0) -372 =-372 Thus, y-intercept is 372. For, no production, the owner had a loss of 372

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Step 2

b)Find the x-intercept(s) and explain what they mean in this con...

p(x)0
8x+0.3x-.0013x-372 0
x25.23, x45.22,x 250.76
lies in [0,225
25
The profit will be zero at approximately x 25
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p(x)0 8x+0.3x-.0013x-372 0 x25.23, x45.22,x 250.76 lies in [0,225 25 The profit will be zero at approximately x 25

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Equations and In-equations