The graph shows the marginal cost C'(x) and the marginal revenue R'(x) for producing x items. Th

(a) The marginal revenue function R'(x) is the derivative of the revenue function R(x). Since th

The graph shows the marginal cost C'(x) and the marginal...

The graph shows the marginal cost C'(x) and the marginal revenue R'(x) for producing x items. The horizontal line is the graph of the marginal revenue R'(x). (a) Write formulas for the revenue function and the marginal revenue function and interpret. (b) Graph the marginal profit function. (c) Graph a possible profit function. R'(x) = [ ]. The selling price of each item is $ [ ]. R(x) = [ ] (b) Graph the marginal profit function. (c) Sketch a possible graph of the profit graph P(x).

Transcript

00:01 In this question we have been given the graph which shows the marginal cost and the marginal revenue for producing x items.

00:08 Okay, so as you can see in the graph, there are two curve given.

00:12 One represents the marginal revenue and another represent the marginal cost.

00:18 The horizontal line represent the marginal revenue.

00:21 So this horizontal line representing the marginal revenue and this represents the marginal cost.

00:31 We need to find out revenue on marginal function then we need to find out the graph of marginal profit and the possible profit function okay so let us see how can we do this so from graph from graph it is quite clear that marginal revenue okay marginal revenue which is r dash of x that is equal to a constant function equal to phi and marginal cost okay, and the marginal cost function which is denoted by c -dash of x, it is given to be a parabola.

01:16 So it's vertex is at 7.

01:19 So parabola is given by x minus 7, 4 square, correct? now you see, now we can find out the profit function.

01:29 Okay.

01:30 So this we got as the marginal revenue and the marginal cost.

01:36 We need to find out revenue and the marginal function so let us see the part a correct so revenue let's say revenue function is denoted by r of x so that will be what it will be integral of r dash of x d x correct so that will be integral of 5 d x so which is equal to r x equal to 5x so this will be my revenue function now we need to find out what is the what we need to find out second thing which is the marginal function.

02:20 So marginal cost function we know, correct, marginal cost function we know and this we got as rx equal to 5x...

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