X =The revenue of a company is given by the function R(n) = (49 - 0.2)n where n

Question

X =The revenue of a company is given by the function R(n) = (49 - 0.2)n where n is the number of items sold and R is the revenue in dollar|

The company's total costs are given by the function C(n) = 2600 + 5.95n where n is the number of items produced and C is the cost in dollars

The company can produce no more than 500 items

Enter the function in Y1 and Y2 so; X = _______________

Y1 = _____________

Y2=___________

b. What is an appropriate viewing to use to see the graph of these functions?

Xmin =_______
Ymin=_____

Xmax =_______
Ymax=__________
Xscl:_________
Yscl:______

c. Determine how many items the company must produce, and how many they must ell to break even (round to the nearest whole number)

d. Over what interval of the domain will the company Make a profit? Write your answer using appropriate mathmatics symbols and then explain the answer in a complete contextual sentence.

Explanation / Answer

a) As per the standard terminologies

X= Number of units sold

Y1= 2600 + 5.95*X ... (Cost)

Y2 = (49-0.2)*X ... (Revenue)

= 48.8*X

b) As given above Max (X) = 500. So

Domain (X)=[0,500]

Hence lower and upper limits for Y1 and Y2 is

Domain (Y1)=[2600,5575]

Domain (Y2)=[0,24400]

For appropriate graphical viewing based on above domains

Xmin=0, Xmax =500, Xscl =25

Ymin=0,Ymax=25000,Yscl=1000

c) For breakeven Y2-Y1 =0

Hence

48.8*X-2600-5.95*X =0

42.85*X = 2600

X ~ 61

So 61 units must be produced and sold to reach breakeven

d) As per the given equations

FC= $2600 ... (Fixed cost)

Vc = $5.95 .... (Variable Cost)

Up = $48.20

Breakeven point Q= FC/(Up-Vc)

=2600/(48.8-5.95)

=60.676

Hence for the domain X in [60.676,500] the company makes a profit. Upper limit is 500 as given in the problem.

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