Use algebraic methods to find where Yaseen’s demand and supply functio

n2z1emldk

n2z1emldk

Answered question

2021-11-29

Use algebraic methods to find where Yaseen’s demand and supply functions intersect. What does this point(s) represent in the context of this problem? Show all your work.
Given that the monthly demand for her painting kits is given by
f(x)=0.02(x100)2, 0x85
Also the supply by Yaseen for each month is given by
g(x)=0.01x2+0.5x, 0x100

Answer & Explanation

Jeffrey Parrish

Jeffrey Parrish

Beginner2021-11-30Added 15 answers

Step 1
It required to algebraically find intersection of Yaseen's demand and supply function.
Equate the given demand and supply function.
0.02(x100)2=0.01x2+0.5x
0.02(x2+10000200x)=0.01x2+0.5x
0.02x2+2004x=0.01x2+0.5x
0.02x20.01x24x0.5x=200
0.01x24.5x+200=0
On further simplification,
x2450x+20000=0
x=450±(450)24(1)(20000)2
x=450±202500800002
x=450±1225002
x=450±3502
x=8002, 1002
x=400, 50
Thus, the x values are 50 and 400.
Step 2
Since x=400 does not satisfy both the condition of demand and supply function the equilibrium quantity is x=50.
Substitute 50 for x in the demand equation.
f(x)=0.02(x100)2
=0.02(50100)2
=0.02(50)2

=0.02×2500
=50
Now substitute 50 for x in the supply equation.
g(x)=0.01x2+0.5x
=0.01(50)2+0.5(50)
=0.01(2500)+0.5(50)
=25+25
=50
It is observed that at x=50 the demand and the supply are equal.That is for 50 painting kits the monthly demand and the amount she can supply yields the same price.

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