2x-y+z=9 x+y-2z=-1 -x+2y+2z=-5

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $138. The quantity demanded each mon

Stells [14]

Answer:

(a) $D(q)=\frac{-1}{25} q+148$

(b) $S(q)=\frac{1}{50}q+58$

(c) $p_{*} =88\\\\q_{*} =1500$

Step-by-step explanation:

(a) For the demand equation D(q) we have

P1: 138 Q1: 250

P2: 108 Q2: 1000

We can find m, which is the slope of the demand equation,

$m=\frac{p_{2} -p_{1} }{q_{2} -q_{1} }=\frac{108-38}{1000-250} =\frac{-30}{750}=\frac{-1}{25}$

and then we find b, which is the point where the curve intersects the y axis.

We can do it by plugging one point and the slope into the line equation form:

$y=mx+b\\\\D(q)=mq+b\\\\138=\frac{-1}{25}(250) +b\\\\138=-10+b\\\\138+10=b=148$

With b: 148 and m: -1/25 we can write our demand equation D(q)

$D(q)=\frac{-1}{25} q+148$

(b) to find the supply equation S(q) we have

P1: 102 Q1: 2200

P2: 102 Q2: 700

Similarly we find m, and b

$m=\frac{p_{2} -p_{1} }{q_{2} -q_{1} }=\frac{72-102}{700-2200} =\frac{-30}{-1500}=\frac{1}{50}$

$y=mx+b\\\\D(q)=mq+b\\\\72=\frac{1}{50}(700) +b\\\\72=14+b\\\\72-14=b=58\\$

And we can write our Supply equation S(q):

$S(q)=\frac{1}{50}q+58$

(c) Now we may find the equilibrium quantity q* and the equilibrium price p* by writing D(q)=S(q), which means the demand equals the supply in equilibrium:

$D(q)=S(q)\\\\\frac{-1}{25}q+148=\frac{1}{50}q+58\\\\$

$148-58=\frac{1q}{50} +\frac{1q}{25} \\\\90= \frac{1q}{50} +\frac{2q}{50}\\\\90=\frac{3q}{50}\\ \\q=1500\\\\$

We plug 1500 as q into any equation, in this case S(q) and we get:

$S(q)=\frac{1}{50}q+58\\\\S(1500)=\frac{1}{50}(1500)+58\\\\S(1500)=30+58\\\\S(1500)=88$

Which is the equilibrium price p*.

8 0

3 years ago

A restaurant offers 4 pasta meals, 5 seafood meals, and 6 burgers for its main courses. If a diner picks a meal at random, what

jeka94

Answer: 5/15 or 1/3 reduced

hope this helps :)

8 0

3 years ago

Help me plz on the question thx

GrogVix [38]

1/2 is the answer. I hope this helps

4 0

4 years ago

ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of B after both reflections?A. (-7, -

Dima020 [189]

Answer:

The correct option is C.

Step-by-step explanation:

From the given figure it is noticed that the coordinates of B are (-5,-7).

If ABC is reflected across x = 1, then

$(x,y)\rightarrow(1-(x-1),y)$

$(x,y)\rightarrow(2-x,y)$

$(-5,-7)\rightarrow(2+5,-7)$

$(-5,-7)\rightarrow(7,-7)$

If ABC is reflected across y =-3.

$(x,y)\rightarrow(x,-3-(y-(-3)))$

$(x,y)\rightarrow(x,-6-y)$

$(7,-7)\rightarrow(7,-6-(-7))$

$(7,-7)\rightarrow(7,1)$

Therefore option C is correct.

8 0

3 years ago

WILL MARK BRAINLIEST IF YOU DONT KNOW DONT ANSWER

rodikova [14]

Answer:

y=20

Step-by-step explanation:

3 0

4 years ago

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