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You sell and produce doodads. Your profit when you sell x thousand doodads is P (x) = -0.4x² + 5x – 7 thousand dollars. What is the largest quantity at which you break even? ANSWER: x = thousand doodads Do not include units in the answer box. Just a number. If rounding is necessary, round to three digits after the decimal.

You sell and produce doodads. Your profit when you sell x thousand doodads is P (x) = -0.4x² + 5x – 7 thousand dollars. What is the largest quantity at which you break even? ANSWER: x = thousand doodads Do not include units in the answer box. Just a number. If rounding is necessary, round to three digits after the decimal.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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q 12 I also attached our formula sheet thank you!

You sell and produce doodads. Your profit when you sell x thousand doodads is P (x) = -0.4x² + 5x – 7 thousand dollars. What is the largest quantity at which you break even? ANSWER: x = thousand doodads Do not include units in the answer box. Just a number. If rounding is necessary, round to three digits after the decimal.
Transcribed Image Text:You sell and produce doodads. Your profit when you sell x thousand doodads is P (x) = -0.4x² + 5x – 7 thousand dollars. What is the largest quantity at which you break even? ANSWER: x = thousand doodads Do not include units in the answer box. Just a number. If rounding is necessary, round to three digits after the decimal.
Suppose you produce and sell Things. The following table summarizes the terms we've learned so far relating to revenue and cost. Assume you are given a graph of total cost TC(q) and total revenue TR(q) for producing and selling q Things. Related equations Graphical Interpretation Term Definition and formulas the total amount you total cost spend to produce q Things TC(q) = VC(q) + FC TC(q) the money you spend to produce q Things without including fixed variable cost VC(q) = TC(q) – FC the graph of VC has the same shape as TC and goes through the origin VC(q) costs the money you must spend even if you produce 0 Things; also known as overhead FC = TC(q) - VC(q) FC = TC(0) fixed cost the vertical distance between the FC TC and VC graphs OR the "y"-intercept of the TC graph average cost AC(q) total cost averaged over the number of Things produced the slope of the diagonal line through the TC graph at q TC(q) AC (q) q variable cost averaged average variable cost the slope of the diagonal line through the VC graph at q over the number of AVC(q) VC(q) AVC(q) Things produced the slope of the least steep diagonal line that intersects the TC graph the smallest value of breakeven price ВЕР average cost the slope of the least steep diagonal line that intersects the VC graph shutdown price the smallest value of SDP average variable cost marginal cost MC(q) (see footnote) the incremental rate of the slope of the secant line through TC (or VC) at q and q +1 MC(q) = TC(q+1)-TC(q) change in TC from q to q+1 Things the total amount you total revenue receive when you sell q Things TR(q) total revenue averaged the slope of the diagonal line through the TR graph at q average revenue over the number of TR(q) AR(q) AR(q) Things sold; also known as price per Thing marginal revenue MR(q) (see footnote) the incremental rate of the slope of the secant line through the TR graph at q and q+1 MR(q) TR(g+1)–TR(g) change in TR from q to q +1 Things the money you are left with after subtracting the vertical distance profit P(q) P(q) = TR(q) – TC(q) between TR and TC total cost from total (when TR> TC) revenue NOTE: If q is measured in hundreds or thousands of Things, the definitions, formulas, and graphical inter- pretations of marginal revenue and marginal cost must be adjusted appropriately.
Transcribed Image Text:Suppose you produce and sell Things. The following table summarizes the terms we've learned so far relating to revenue and cost. Assume you are given a graph of total cost TC(q) and total revenue TR(q) for producing and selling q Things. Related equations Graphical Interpretation Term Definition and formulas the total amount you total cost spend to produce q Things TC(q) = VC(q) + FC TC(q) the money you spend to produce q Things without including fixed variable cost VC(q) = TC(q) – FC the graph of VC has the same shape as TC and goes through the origin VC(q) costs the money you must spend even if you produce 0 Things; also known as overhead FC = TC(q) - VC(q) FC = TC(0) fixed cost the vertical distance between the FC TC and VC graphs OR the "y"-intercept of the TC graph average cost AC(q) total cost averaged over the number of Things produced the slope of the diagonal line through the TC graph at q TC(q) AC (q) q variable cost averaged average variable cost the slope of the diagonal line through the VC graph at q over the number of AVC(q) VC(q) AVC(q) Things produced the slope of the least steep diagonal line that intersects the TC graph the smallest value of breakeven price ВЕР average cost the slope of the least steep diagonal line that intersects the VC graph shutdown price the smallest value of SDP average variable cost marginal cost MC(q) (see footnote) the incremental rate of the slope of the secant line through TC (or VC) at q and q +1 MC(q) = TC(q+1)-TC(q) change in TC from q to q+1 Things the total amount you total revenue receive when you sell q Things TR(q) total revenue averaged the slope of the diagonal line through the TR graph at q average revenue over the number of TR(q) AR(q) AR(q) Things sold; also known as price per Thing marginal revenue MR(q) (see footnote) the incremental rate of the slope of the secant line through the TR graph at q and q+1 MR(q) TR(g+1)–TR(g) change in TR from q to q +1 Things the money you are left with after subtracting the vertical distance profit P(q) P(q) = TR(q) – TC(q) between TR and TC total cost from total (when TR> TC) revenue NOTE: If q is measured in hundreds or thousands of Things, the definitions, formulas, and graphical inter- pretations of marginal revenue and marginal cost must be adjusted appropriately.
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