Question 577875
Let {{{a}}} = acres planted in corn
Let {{{b}}} = acres planted in wheat
given:
(1) {{{ a + b = 4500 }}}
(2) {{{ 42a + 35b = 165200 }}}
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The solution has to be on the line
(1) in an area where (2) is true
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(1) {{{ b = 4500 - a }}}
Substitute (1) into (2)
(2) {{{ 42a + 35*( 4500 - a ) = 165200 }}}
(2) {{{ 42a + 157500 - 35a = 165200 }}}
(2) {{{ 7a <= 165200 - 157500 }}}
(2) {{{ 7a = 7700 }}}
(2) {{{ a = 1100 }}}
And, from (1)
(2) {{{ 4500 - b = 1100 }}}
(2) {{{ -b = - 3400 }}}
(2) {{{ b = 3400 }}}
1100 acres should be planted in corn
3400 acres should be planted in wheat
here's the plots:
{{{ graph( 600, 600, -500, 5000, -500, 5000, 4500 - x, -(42/35)*x + 4720  ) }}}