Problema Solution
A manufacturer of toy dolls can supply 2000 dolls if the dolls are sold at $8 each, but he can supply only 800 dolls if the dolls are sold at $2 each. If x represents the price of dolls an y the number of items, write an equation for the supply curve.
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Assuming that the equation of the supply curve is linear we can write:
y = ax + b, where a and b are constants that we need to find
for y = 2000 dolls, x = $8 or:
2000 = 8a + b
8a + b = 2000
for y = 800 dolls, x = $2 or:
800 = 2a + b
2a + b = 800
by solving the system of equations
8a + b = 2000
2a + b = 800
we find
a = 200
b = 400
click here to see the step by step solution of the system of equations
the equation of the supply curve is:
y = 200x + b.
Assuming that the equation of the supply curve is linear we can write:
y = ax + b, where a and b are constants that we need to find
for y = 2000 dolls, x = $8 or:
2000 = 8a + b
8a + b = 2000
for y = 800 dolls, x = $2 or:
800 = 2a + b
2a + b = 800
by solving the system of equations
8a + b = 2000
2a + b = 800
we find
a = 200
b = 400
click here to see the step by step solution of the system of equations
the equation of the supply curve is:
y = 200x + 400.