(section 2. 2) This is another question from my math homework due at 5, and I have attached my equation "cheat-sheet" please help me! 318.4 SummarySuppose you produce and sell Things. The following table summarizes the terms we'velearned so far relating to revenue and cost. Assume you are given a graph of total costTC(q) and total revenue TR(q) for producing and selling q Things.GraphicalInterpretationRelated equations andTermDefinitionformulasthe total amount you spendto produce q Thingstotal costTC(q) = V C(q)+ FCTC(q)the money you spend toproduce q Things withoutincluding fixed coststhe graph of VC has thesame shape as TC and goesthrough the originvariable costVC(q) = TC(q) – FCVC(q)the money you must spendeven if you produce 0 Things;the vertical distance betweenFC = TC(q) – VC(q)FC = TC(0)fixed costthe TC and VC graphs OR the"y"-intercept of the TC graphFCalso known as overheadaverage costAC(q)total cost averaged over thenumber of Things producedthe slope of the diagonal linethrough the TC graph at qTC(q)AC(q)averagevariable costvariable cost averaged overthe number of Thingsproducedthe slope of the diagonal linethrough the VC graph at qVC(q)AVC(q)AV C(q)the slope of the least steepdiagonal line that intersectsthe TC graphthe slope of the least steepdiagonal line that intersectsthe VC graphthe slope of the secant linethrough TC (or VC) at qand q+1breakeventhe smallest value of averagepriceВЕРcostshutdownthe smallest value of averagepricevariable costSDPmarginal costMC(q)(see footnote)the incremental rate of(q+1)—ТC(q)MC(q)change in TC from q to q+ 1Thingstotal revenuethe total amount you receivewhen you sell q ThingsTR(q)averagetotal revenue averaged over thenumber of Things sold; alsoknown as price per Thingthe slope of the diagonal linethrough the TR graph at qTR(q)AR(q)revenueAR(q)the slope of the secant linethrough the TR graph at qand q+1the incremental rate ofmarginalrevenue MR(q) | change in TR from q to q +1(see footnote)MR(q)TR(q+1)–TR(g)Thingsthe vertical distance betweenprofitP(q)the money you are left withafter subtracting total costfrom total revenueTR and TC (whenTR>TC)P(q) = TR(q) – TC(q)NOTE: If q is measured in hundreds or thousands of Things, the definitions, formulas, andgraphical interpretations of marginal revenue and marginal cost must be adjusted appro-priately. You sell Blivets on a sliding-price scale. Price per Blivet p in dollars is given by a linear function of q Blivets. You charge $24 each for an order of 1 Blivet and $18 each for an order of 13 Blivets.a.) Find the linear formula for price per Blivet as a function of quantity q.p=b.) Write out the formula for your total revenue for an order of q Blivets.TR(q)=TR(q+1)-TR(q)c.) Recall that marginal revenue at q is given by MR(q)=-and compute the marginal revenue for selling 10 Blivets.dollars per Blivetd.) The Blivets cost $5 each to manufacture and you have fixed costs of $100. Give the formula for the total cost to produce q Blivets.TC(q)=e.) What is the maximum profit? Include units. (Assume that you cannot sell a fraction of a Blivet. The quantity that maximizes profit must be a whole number.)

Answered: a.) Find the linear formula for price…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(section 2. 2) This is another question from my math homework due at 5, and I have attached my equation "cheat-sheet" please help me!

31
8.4 Summary
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.
Graphical
Interpretation
Related equations and
Term
Definition
formulas
the total amount you spend
to produce q Things
total cost
TC(q) = V C(q)+ FC
TC(q)
the money you spend to
produce q Things without
including fixed costs
the graph of VC has the
same shape as TC and goes
through the origin
variable cost
VC(q) = TC(q) – FC
VC(q)
the money you must spend
even if you produce 0 Things;
the vertical distance between
FC = TC(q) – VC(q)
FC = TC(0)
fixed cost
the TC and VC graphs OR the
"y"-intercept of the TC graph
FC
also known as overhead
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)
average
variable cost
variable cost averaged over
the number of Things
produced
the slope of the diagonal line
through the VC graph at q
VC(q)
AVC(q)
AV C(q)
the slope of the least steep
diagonal line that intersects
the TC graph
the slope of the least steep
diagonal line that intersects
the VC graph
the slope of the secant line
through TC (or VC) at q
and q+1
breakeven
the smallest value of average
price
ВЕР
cost
shutdown
the smallest value of average
price
variable cost
SDP
marginal cost
MC(q)
(see footnote)
the incremental rate of
(q+1)—ТC(q)
MC(q)
change in TC from q to q+ 1
Things
total revenue
the total amount you receive
when you sell q Things
TR(q)
average
total revenue averaged over the
number of Things sold; also
known as price per Thing
the slope of the diagonal line
through the TR graph at q
TR(q)
AR(q)
revenue
AR(q)
the slope of the secant line
through the TR graph at q
and q+1
the incremental rate of
marginal
revenue MR(q) | change in TR from q to q +1
(see footnote)
MR(q)
TR(q+1)–TR(g)
Things
the vertical distance between
profit
P(q)
the money you are left with
after subtracting total cost
from total revenue
TR and TC (when
TR>TC)
P(q) = TR(q) – TC(q)
NOTE: If q is measured in hundreds or thousands of Things, the definitions, formulas, and
graphical interpretations of marginal revenue and marginal cost must be adjusted appro-
priately.

You sell Blivets on a sliding-price scale. Price per Blivet p in dollars is given by a linear function of q Blivets. You charge $24 each for an order of 1 Blivet and $18 each for an order of 13 Blivets.
a.) Find the linear formula for price per Blivet as a function of quantity q.
p=
b.) Write out the formula for your total revenue for an order of q Blivets.
TR(q)=
TR(q+1)-TR(q)
c.) Recall that marginal revenue at q is given by MR(q)=-
and compute the marginal revenue for selling 10 Blivets.
dollars per Blivet
d.) The Blivets cost $5 each to manufacture and you have fixed costs of $100. Give the formula for the total cost to produce q Blivets.
TC(q)=
e.) What is the maximum profit? Include units. (Assume that you cannot sell a fraction of a Blivet. The quantity that maximizes profit must be a whole number.)

Expert Solution

part a

By bartleby rules only first three subparts have been answered

Given that $p$ is the price per blivet and number of blivets to sell is $q$

Price for an order of 1 blivet is $24 and that for an order of 13 blivets is $18.

Since $p$ is a function of $q$ , therefore,

$\begin{array}{rcl} p (1) & = & 24 \\ p (13) & = & 18 \end{array}$

So, the line passes through the points (1,24) and (13,18).

Slope of the line is

$\begin{array}{rcl} m & = & \frac{24 - 18}{1 - 13} \\ = & - \frac{6}{12} \\ = & - \frac{1}{2} \end{array}$

Therefore, equation of the line is

$\begin{array}{rcl} (p - 1) & = & - \frac{1}{2} (q - 24) \\ p & = & - 0.5 q + 13 \end{array}$

Hence, $p$ can be expressed as $\begin{array}{rcl} p \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} - \end{array} \begin{array}{rcl} 0 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 5 \end{array} \begin{array}{rcl} q \end{array} \begin{array}{rcl} + \end{array} \begin{array}{rcl} 13 \end{array}$

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