Question

The marginal revenue for x of a certain industrial machine is dollars per year and the marginal cost of the industrial machines is dollars per year.

Find the Marginal Profit for 4 industrial machines. Interpret MP(4) in economic terms.

Sketch a graph of the marginal profit function. Carefully label the function and the y intercept. Meaningfully label the x and y axes.

On the above graph, shade the area that represents the profit generated from the production and sale of from 7 to 20 industrial machines.

In the space below, give the definite integral for the shaded region and interpret what your shading represents (Don’t forget to use appropriate units.)

Give and solve (using the Fundamental Theorem of Calculus) the definite integral that represents the profit from the production and sale of from 7 to 20 industrial machines.

The profit from the production and sale of 1 industrial machine is $25,000. What is the general profit equation for the industrial machines? How much will the company profit from the production and sale of 3 industrial machines?

Answer 1

Sridustrial machine dcucnue Бооо - 8 marginad COst 3500 t13n2 Mangiad Soo-8n-3500 t 13nj DMarginal prafit Cost revenue- 2 1500- 31 Nos 500- 4) Magihal freie 60 m.argin pris posikive The =4 us moye Hhan vevenue he arginal So eeon Cost im hare to increate he froduetion Emarginad rca enue : 20 Manginajijumckien 2 5o0-21

S let aJume 15o-a Lo maginal forglin So Sholos he Tntergation whaled egion (1500 -31x)d )- Ce600-(8010)) 50ox 2 26000 $24.049o The ir smaking dos s im C<n< ?0)