Profit loss analysis. Use the revenue and cost functions from Problem 63 in this exercise: where x is in millions of chips, and R(x) and C(x) are in millions of dollars. Both functions have domain (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 to the nearest thousand chips.
where x is in millions of chips, and R(x) and C(x) are in millions of dollars. Both functions have domain 
(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 to the nearest thousand chips.
(D) Refer to the graph drawn in part (A). Does the maximum profit appear to occur at the same value of x as the maximum revenue? Are the maximum profit and the maximum revenue equal? Explain. (E) Verify your conclusion in part
(D) by finding the value of x (to the nearest thousand chips) that produces the maximum profit. Find the maximum profit (to the nearest thousand dollars)
Problem 63
Break-even analysis. Use the revenue function from Problem 61 in this exercise and the given cost function:
where x is in millions of chips, and R(x) and C(x) are in millions of dollars. Both functions have domain 1 
x 20.
(A) Sketch a graph of both functions in the same rectangular coordinate system.
(B) Find the break-even points to the nearest thousand chips.
(C) For what values of x will a loss occur? A profit?
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