Yaseen estimates that the mounthly demand for her painting kits can be

alka8q7

alka8q7

Answered question

2021-12-07

Yaseen estimates that the mounthly demand for her painting kits can be modeled by the function
f(x)=0.02(x100)2
where 0x85
The number of kits that Yaseen can supply each month is modeled by the function g(x)=0.01x2+0.5x, where 0x100. The value of x represents the quantity of kits and the output of each function is the price.
Use this information and what you know about quadratic functions and system of non-linear equations to explore the questions below.
Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario?

Answer & Explanation

James Etheridge

James Etheridge

Beginner2021-12-08Added 16 answers

Step 1 
Price and demand relationships.
f(x)=0.02(x100)2 
x quantly if kit, 0x85 
Fer x=0 demand or no demand price 
f(0)=0.02×1002=200 
x=85 haytest demand price 
f(85)=0.02×152=4.5 
Price demand 200 to 4.5 
demand 0 to 85 
Step 2 
Supply function 
g(x)=0.01x2+0.5x 
x=0 
g(0)=0 price 
x=100 
g(100)=0.01×1002+0.5×100 
=150 price 
As the quantity of x or paint increases, the price of the supply rises.

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