Please answer every part of the question in the images below.
The pharmaceutical company CVL produces a new antidepressant drug. During production, CVL finds that their total costs increase at a rate of $14.85 per case. They also know that the total production cost is $3,450.20 when 52 cases of the drug are produced. CVL will sell each case of the drug for $46.04 . Let d represent the number of cases of the drug produced or sold by CVL. Then C is the total production cost (in dollars), R is the total revenue (in dollars), and P is the total profit earned (in dollars) from the cases of the antidepressant drug.
cases of the drug are produced. CVL will sell each case of the drug for $46.04. antidepressant drug. (a) Assume C(d) is a linear function. Based on the information given above, since C(d) is linear, the slope of the graph of the line must be (b) Use the slope of C and the given total cost when 52 cases of the drug are produced to find the equation of the line. Then, use the equation to complete the following: The fixed costs for the drug production are $ The cost function is C()= To visualize CVL's cost function in the graph, enter the slope and intercept into the appropriate boxes in the applet above. (c) Suppose d=108 for this part of the question. Use the answers above to complete the following. Round dollar amounts to the nearest cent. If CVL produces cases of their antidepressant drug, their total production costs will be At this production level, the average cost to produce the drug is (d) Find CVL's revenue function and profit function. Both will be linear. Simplify the profit function into slope-intercept form. The revenue function is R()= The profit function is P()= To visualize CVL's revenue and profit functions in the graph, enter the slopes and intercepts into the appropriate boxes in the applet above. You should now see graphs of all three lines. (e) Fill in the blanks to find the marginal revenue function and interpret the marginal revenue. The marginal revenue function is MR()= The marginal revenue is the of CVL's revenue model. The units of marginal revenue in this application will be Thus, CVL's revenue will increase by for every additional (f) If CVL produces and sells 108 cases of the drug, this will result in a total net profit of This means that when 108 cases are produced and sold, the average profit is (g) Find the break-even point and round appropriately to complete the following sentence. CVL must produce and sell cases of the antidepressant drug in order to break even. cases of the drug are produced. CVL will sell each case of the drug for $46.04. antidepressant drug. (a) Assume C(d) is a linear function. Based on the information given above, since C(d) is linear, the slope of the graph of the line must be (b) Use the slope of C and the given total cost when 52 cases of the drug are produced to find the equation of the line. Then, use the equation to complete the following: The fixed costs for the drug production are $ The cost function is C()= To visualize CVL's cost function in the graph, enter the slope and intercept into the appropriate boxes in the applet above. (c) Suppose d=108 for this part of the question. Use the answers above to complete the following. Round dollar amounts to the nearest cent. If CVL produces cases of their antidepressant drug, their total production costs will be At this production level, the average cost to produce the drug is (d) Find CVL's revenue function and profit function. Both will be linear. Simplify the profit function into slope-intercept form. The revenue function is R()= The profit function is P()= To visualize CVL's revenue and profit functions in the graph, enter the slopes and intercepts into the appropriate boxes in the applet above. You should now see graphs of all three lines. (e) Fill in the blanks to find the marginal revenue function and interpret the marginal revenue. The marginal revenue function is MR()= The marginal revenue is the of CVL's revenue model. The units of marginal revenue in this application will be Thus, CVL's revenue will increase by for every additional (f) If CVL produces and sells 108 cases of the drug, this will result in a total net profit of This means that when 108 cases are produced and sold, the average profit is (g) Find the break-even point and round appropriately to complete the following sentence. CVL must produce and sell cases of the antidepressant drug in order to break even
