Profit-loss analysis. Use the revenue and cost functions from Problem 66: R x = x 2 , 000 − 60 x Revenue function C x = 4 , 000 + 500 x Cost function where x is thousands of computers, and R x and C x are in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25 . (A) Form a profit function P , and graph R , C , and P in the same rectangular coordinate system . (B) Discuss the relationship between the intersection points of the graphs of R and C and the x intercepts of P . (C) Find the x intercepts of P and the break-even points. (D) Refer to the graph drawn in part (A). Does the maximum profit appear to occur at the same value of x as the maxi- mum revenue? Are the maximum profit and the maximum revenue equal? Explain. (E) Verify your conclusion in part (D) by finding the value of x that produces the maximum profit. Find the maxi- mum profit and compare with Problem 66B.
Profit-loss analysis. Use the revenue and cost functions from Problem 66: R x = x 2 , 000 − 60 x Revenue function C x = 4 , 000 + 500 x Cost function where x is thousands of computers, and R x and C x are in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25 . (A) Form a profit function P , and graph R , C , and P in the same rectangular coordinate system . (B) Discuss the relationship between the intersection points of the graphs of R and C and the x intercepts of P . (C) Find the x intercepts of P and the break-even points. (D) Refer to the graph drawn in part (A). Does the maximum profit appear to occur at the same value of x as the maxi- mum revenue? Are the maximum profit and the maximum revenue equal? Explain. (E) Verify your conclusion in part (D) by finding the value of x that produces the maximum profit. Find the maxi- mum profit and compare with Problem 66B.
Profit-loss analysis. Use the revenue and cost functions from Problem 66:
R
x
=
x
2
,
000
−
60
x
Revenue function
C
x
=
4
,
000
+
500
x
Cost function
where
x
is thousands of computers, and
R
x
and
C
x
are in thousands of dollars. Both functions have domain
1
≤
x
≤
25
.
(A) Form a profit function P, and graph
R
,
C
,
and
P
in the same rectangular coordinate system.
(B) Discuss the relationship between the intersection points of the graphs of
R
and
C
and the
x
intercepts of
P
.
(C) Find the
x
intercepts of
P
and the break-even points.
(D) Refer to the graph drawn in part (A). Does the maximum profit appear to occur at the same value of
x
as the maxi- mum revenue? Are the maximum profit and the maximum revenue equal? Explain.
(E) Verify your conclusion in part (D) by finding the value of
x
that produces the maximum profit. Find the maxi- mum profit and compare with Problem 66B.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
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