Question 1123071
{{{ x = a*p + b }}}
You are given 2 points on a straight line, ( p,x )
This is the order because x depends on p
( 10, 1360 )
( 20, 510 )
{{{ 1360 = a*10 + b }}}
{{{ 10a + b = 1360 }}}
and
{{{ 510 = a*20 + b }}}
{{{ 20a + b = 510 }}}
————————————
By subtraction:
{{{ 10a = - 850 }}}
{{{ a = -85 }}}
And
{{{ 10*(-85) + b = 1360 }}}
{{{ b = 2210 }}}
The equation is:
{{{ x = -85p + 2210 }}}
———————————-
At {{{ p = 16 }}}
{{{ x = -85*16 + 2210 }}}
{{{ x = 2210 - 1360 }}}
{{{ x = 850 }}} will be sold
—————————————-
At {{{ x = 1020 }}}
{{{ 1020 = -85*p + 2210 }}}
{{{ 85p = 1190 }}}
{{{ p = 14 }}}
N$14
—————————————-
The max price will result in 0 sold, so
{{{ 0 = -85p + 2210 }}}
{{{ p = 26 }}}
N$26 is maximum price