Question 1185004: Suppose that a manufacturer will place 1000 units of a product on the market when the price is $10 per unit, and 1400 units when the price is $12 per unit. Find the supply equation for the product assuming the price p and quantity q are linearly related.
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
Suppose that a manufacturer will place 1000 units of a product on the market when the price is $10 per unit,
and 1400 units when the price is $12 per unit.
Find the supply equation for the product assuming the price p and quantity q are linearly related.
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The equation for supply is of the form
q = c + d*p,
where q is the quantity of items, produced and sold, while p is the price for single unit of production.
"c" and "d" are coefficients; in our consideration, they assumed to be constant.
You can approach this problem formally. You have a straight line and two given points in it, (10,1000) and (12,1400),
and your task is to construct the appropriate linear function.
Then you write the standard interpolation-extrapolation equation
q =  + 
and substitute there given values  = 10,  = 12, = 1000,  = 1400. You will get then
q = 1000 +  = 1000 +  = 1000 + 200*(p-10),
so the final form of your supply equation is
q = 1000 + 200*(p-10), or, EQUIVALENTLY, q = 200p - 1000. ANSWER
Solved.
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