Mathematics, 29.01.2020 03:09 wytchnia

Agroup of retailers will buy 104 televisions from a wholesaler if the price is $300 and 144 if the price is $250. the wholesaler is willing to supply 88 if the price is $225 and 168 if the price is $315. assuming the resulting supply and demand functions are linear, find the equilibrium point for the market.

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Answer from: denaemarie02

The equilibrium point will be around 128 units, which will be supplied and demanded at an equilibrium price of $ 270.

Since a group of retailers will buy 104 televisions from a wholesaler if the price is $ 300 and 144 if the price is $ 250, while the wholesaler is willing to supply 88 if the price is $ 225 and 168 if the price is $ 315, assuming the resulting supply and demand functions are linear, to find the equilibrium point for the market the following calculation must be performed:

(300 - 250) / (144 - 104) = X 50/40 = X 1.25 = X Thus, the retailers will buy one more television for every $ 1.25 of sale. (315 - 225) / (168 - 88) = X 90/80 = X 1.125 = X In turn, the wholesaler will supply one less television for every $ 1,125 of discount. 116 x (300 - 12 x 1.25) = X 116 x 285 = X 33060 = X 116 x (225 + 28 x 1.125) = X 116 x 256.5 = X 29754 = X 126 x (300 - 22 x 1.25) = X 126 x 272.5 = X 34335 = X 126 x (225 + 38 x 1.125) = X 126 x 267.75 = X 33736.5 = X 128 x (300 - 24 x 1.25) = X 128 x 270 = X 34560 = X 128 x (225 + 40 x 1.125) = X 128 x 270 = X 34560 = X

Therefore, the equilibrium point will be around 128 units, which will be supplied and demanded at an equilibrium price of $ 270.

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Answer from: amelvin41

(275,122)

When the price will be $275, the quantity will be 122 televisions.

Step-by-step explanation:

We have been given that a group of retailers will buy 104 televisions from a wholesaler if the price is $300 and 144 if the price is $250.

As the quantity of televisions depends on price of televisions, so our demand curve will pass through points (300,104) and (250,144).

Let us find slope of demand line using slope formula.

$m=\frac{y_2-y_1}{x_2-x_1}$ , where,

$m =\text{Slope of line}$ ,

$y_2-y_1=\text{Difference between two y-coordinates}$ ,

$x_2-x_1=\text{Difference between same x-coordinates of two y-coordinates}$

Upon substituting coordinates of our given points in slope formula we will get,

$m=\frac{104-144}{300-250}$

$m=\frac{-40}{50}$

$m=-\frac{4}{5}$

Let us substitute $m=-\frac{4}{5}$ coordinates of point (250,144) in slope intercept form of equation ( y=mx+b ).

$144=-\frac{4}{5}*250+b$

144=-4*50+b

144=-200+b

144+200=-200+200+b

344=b

Upon substituting b=344 and $m=-\frac{4}{5}$ we will get equation of our demand line as:

$y=-\frac{4}{5}x+344$

Similarly we will find the equation of supply line using points (225,88) and (315,168).

$m=\frac{168-88}{315-225}$

$m=\frac{80}{90}$

$m=\frac{8}{9}$

Let us substitute $m=\frac{8}{9}$ and coordinates of point (225,88) in slope intercept form of equation ( y=mx+b ).

$88=\frac{8}{9}*225+b$

88=8*25+b

88=200+b

88-200=200-200+b

-112=b

Upon substituting b=-112 and $m=\frac{8}{9}$ we will get equation of our supply line as:

$y=\frac{8}{9}x-122$

Let us equate both lines to find the point where both lines intersect.

$-\frac{4}{5}x+344=\frac{8}{9}x-122$

$-\frac{4}{5}x-\frac{8}{9}x+344=\frac{8}{9}x-\frac{8}{9}x-122$

$-\frac{4}{5}x-\frac{8}{9}x+344=-122$

$-\frac{4}{5}x-\frac{8}{9}x+344-344=-122-344$

$-\frac{4}{5}x-\frac{8}{9}x=-466$

Let us have a common denominator.

$-\frac{4*9}{5*9}x-\frac{8*5}{9*5}x=-466$

$-\frac{36}{45}x-\frac{40}{45}x=-466$

$\frac{-36-40}{45}x=-466$

$\frac{-76}{45}x=-466$

$\frac{-76}{45}*\frac{45}{-76}x=-466*\frac{45}{-76}$

$x=466*\frac{45}{76}$

x=6.1315789473684211*45

$x=275.9210526315789495\approx 275$

Let us substitute x=275 in any of our equation to solve for y.

$y=-\frac{4}{5}*275+344$

y=-4*55+344

y=-220+344

y=122

Therefore, the equilibrium point for the market will be (275,122).

Answer from: Quest

step-by-step explanation:

this is a subtraction problem.

10 - 2 = 8

Answer from: Quest

Could you make it more clear?
This is ! be right about ur ! ! both questions and u

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