. 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?