Y " 70 s=4 A=(4, 45.11) Actual Change B=(5, 61.4) D= (4, 7.29) S % 2 MP(8) B P(s) 13 14 15 16 Sofa King is a fumiture store based in New York that decides to analyze the total profit resulting from the production and sales of their contemporary style sofas. Sofa King's proft model P(s) (in hundreds of dollars) from the sale of a of these sofas is graphed in the applet above (black curve). The applet also shows Sofa King's marginal profit function, MP(s) = P(s) (green curve), as well as the tangent line to P(s) at point A Use the applet to answer the following questions. Note that an input box is provided for you to enter a particular number of sofas. Also observe that point B is one horizontal unit to the right of A (e.g., if point A has z-4, then the point B has z= 5). (a) Find the actual change in profit if Sofa King increases sales from 12 sofas to 13 sofas by filling in the blanks Actual Change in Profit-S This means the total profit decreases by hundred dollars when sales increase from 12 sofas to 13 sofas (b) Translate your answer in part (a) into function notation, using P(s) P (c) Use Sofa King's marginal profit function, P(s) to complete the following When Sofa King sells 12 sofas, their profit is ??? at an approximate rate of hundred dollars per sofa sold. (d) Translate your answer in part (c) into function notation, using P'(s). P'( (e) Observe that your work in parts (a) to (d) illustrates the fact that P(n+1)P(n) + P(n) for n sofas sold. In particular, P(12) + P(12) and P(13) are approximately equal to each other. 70 B s=4 A=(4, 45.11) B=(6,61.4) D=(4,7.29) Actual Change MP(8) P(s) 22 16 Sofa King is a fumiture store based in New York that decides to analyze the total profit resulting from the production and sales of their contemporary style sofas. Sofa King's proft model P(s) (in hundreds of dollars) from the sale of 8 of these sofas is graphed in the applet above (black curve). The applet also shows Sofa King's marginal profit function, MP(s) = P(s) (green curve), as well as the tangent line to P(s) at point A Use the applet to answer the following questions. Note that an input box is provided for you to enter a particular number of sofas. Also observe that point B is one horizontal unit to the right of A (e.g. if point A has 2-4, then the point B has z=5) (a) Find the actual change in profit if Sofa King increases sales from 12 sofas to 13 sofas by filling in the blanks Actual Change in Profit- This means the total profit decreases by hundred dollars when sales increase from 12 sofas to 13 sofas (b) Translate your answer in part (a) into function notation, using P(a). P P (c) Use Sofa King's marginal profit function, P' (a) to complete the following: When Sofa King sells 12 sofas, their proft is ??? at an approximate rate of hundred dollars per sofa sold. (d) Translate your answer in part (c) into function notation, using P' (8) P'( at an approximate rate of hundred dollars per sofa sold (c) Use Sofa King's marginal profit function, P(a) to complete the following When Sota King selts 12 sotas, their profit is ??? (d) Translate your answer in part (c) into function notation, using P(a) P (e) Observe that your work in parts (a) to (d) illustrates the fact that P(n + 1) P(n) + P(n) for n sofas sold. In particular, P(12) + P(12)= P(13) are approximately equal to each other. and