A wood stove and an oil furnace are both used to heat a house. On any given day,
the stove can be used for, at most, 12 hours, and the
furnace can be used for, at
most
8 hours. It costs $1.00/hour to operate the stove, and
it costs $1.50/hour to operate
the furnace. At most, $18.00 can be spent to operate
both for one day. If the stove
produces heat at a rate of 3000 kJ/hour and the furnace
produces heat at a rate of
5000 kJ/hour, how long should each be operated to produce
the maximum amount
of heat?