Question 987504
Let {{{ a }}} = number of clocks produced
during the regular workweek
Let {{{ b }}} = number of clocks priduced
during overtime
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given:
(1) {{{ a + b >= 10000 }}}
(2) {{{ 2a + 3b <= 21000 }}}
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Multiply both sids of (1) by {{{ -3 }}}
(1) {{{ -3a -3b <= -30000 }}}
Add (1) and (2)
{{{ -a <= -9000 }}}
{{{ a >= 9000 }}}
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The minimum number of clocks that must
be produced during the workweek is 9000
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check:
(1) {{{ b >= 1000 }}}
and
(2) {{{ 2*9000 + 3*1000 <= 21000 }}}
(2) {{{ 18000 + 3000 <= 21000 }}}
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Try plotting {{{ b = f(a) }}} for (1)
and (2), and find the area between the
lines that are permitted values of 
{{{ a }}} and {{{ b }}}