16026 company distributes colege logosweatshirts and sells them for sss each. me

Question

16026 company distributes colege logosweatshirts and sells them for sss each. me total cost function is ear, and the total cost for 100 sweatshitsis ss206, whereas the total cost for 2osweatshirts is sz6zs. (a) write the equation for the revenue function Rt). (b) write the equation for the total cost function (e) Find the break-even quantity. Need Help? 16083 If the demand for a pair of shoes isgiven by 2p+ sa poo and the supply function for tis p 20-10, compare the ouantity demanded and the quantity suppled when the price is soo. pairs of shoes quantity supplied pairs of shoes there be a surplus or shortfal at this pricey There wil be a surplus. There w be a shortfall. Need Help? CD

Explanation / Answer

There are two answers for each question. One answer for the case where 100 sweatshirts are purchased and a different answer for the case where 250 sweatshirts are purchased.

100 Sweatshirts
Total Cost = $5206
Cu = Cost per unitt = $5206/100 = $52.06
Ru = Revenue per unit = $55
N = Number of sweatshirts sold
Rt = Total revenue
Ct = Total cost

a) Equation for revenue function
Rt = Ru x N
Rt = $55 x N

b) Equation for total cost function
[NOTE: The "total cost function" here is the "accounting cost." The actual total cost of the sweatshirts is $4360. In order to figure the breakeven, you need to know what the "accounting cost" is, or, in other words, what the "cost per sale" is and so you can figure out net revenues.]
Ct = Cu x N
Ct = $52.06 x N

c) Find the breakeven point
"Breakeven" is defined as the number of units that must be sold so that total revenue equals total cost. In analyzing "breakeven" for this case, the total cost is NOT the "total cost function", but it is the actual total cost (which, is $4360)
Breakeven => Total revenue = Actual total cost
Breakeven => (Ru x N) = $5206
$55N = $5206
N = $5206 / $55
N = 94.6545
(95 units must be sold to recover the $5206 paid for the 100 sweatshirts)

--------------------------

290 Sweatshirts
Total Cost = $7676
Cu = Cost per unitt = $7676/290 = $26.4689
Ru = Revenue per unit = $55
N = Number of sweatshirts sold
Rt = Total revenue
Ct = Total cost

a) Equation for revenue function
Rt = Ru x N
Rt = $55 x N

b) Equation for total cost function
[NOTE: The "total cost function" here is the "accounting cost." The actual total cost of the sweatshirts is $4360. In order to figure the breakeven, you need to know what the "accounting cost" is, or, in other words, what the "cost per sale" is and so you can figure out net revenues.]
Ct = Cu x N
Ct = $26.4689 x N

c) Find the breakeven point
"Breakeven" is defined as the number of units that must be sold so that total revenue equals total cost. In analyzing "breakeven" for this case, the total cost is NOT the "total cost function", but it is the actual total cost (which, is $4360)
Breakeven => Total revenue = Actual total cost
Breakeven => (Ru x N) = $7676
$55N = $7676
N = $7676 / $55
N =139.5636
(140 units must be sold to recover the $7676 paid for the 290 sweatshirts)

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home / study / math / precalculus / questions and answers / if the demand for a pair of shoes is given by 2p ...

If the demand for a pair of shoes is given by
2p + 5q = 300
and the supply function for it is
p 2q = 10,
compare the quantity demanded and the quantity supplied when the price is $90.

2(90) + 5q =300 ==>5q = 300 - 180 ==> 120 ,q =24 and 90 - 2q =10==>- 2q = -80 ==> q =40

quantity demanded __24___- pair of shoes

quantity supplied___40___ pair of shoes

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