Question 1185004
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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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<pre>
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 = {{{q[1]}}} + {{{((q[2]-q[1])/(p[2]-p[1]))*(p-p[1])}}}


and substitute there  given values  {{{p[1]}}}= 10,  {{{p[2]}}} = 12, {{{q[1]}}} = 1000,  {{{q[2]}}} = 1400.  You will get then


    q = 1000 + {{{((1400-1000)/(12-10))*(p-10)}}} = 1000 + {{{(400/2)*(p-10)}}} = 1000 + 200*(p-10),


so the <U>final form of your supply equation</U> is


    q = 1000 + 200*(p-10),   or, EQUIVALENTLY,  q = 200p - 1000.      <U>ANSWER</U>
</pre>

Solved.