【Question 14】
A freight company needs to transport 89 tons of cargo. The load capacity of each large truck is 7 tons, and that of a small truck is 4 tons. If each large truck consumes 14 liters of fuel, and each small truck consumes 9 liters, how many liters of fuel will be consumed at a minimum to transport all this cargo?
【Analysis and Solution】
The problem of extremum.
Since the large truck consumes on average $14 \div 7=2$ liters of fuel per ton of cargo, and the small truck consumes on average $9 \div 4=2.25$ liters of fuel per ton of cargo; therefore, we should use as many large trucks as possible;
$$
89 \div 7=12 \cdots \cdots 5 \text {; }
$$
(1) 13 large trucks: can transport $7 \times 13=91$ tons of cargo, consuming a total of $14 \times 13=182$ liters of fuel;
(2) 12 large trucks, 2 small trucks: can transport $7 \times 12+4 \times 2=92$ tons of cargo, consuming a total of $14 \times 12+9 \times 2=186$ liters of fuel;
(3) 11 large trucks, 3 small trucks: can transport $7 \times 11+4 \times 3=89$ tons of cargo, consuming a total of $14 \times 11+9 \times 3=181$ liters of fuel; the minimum fuel consumption to transport this batch of goods is 181 liters.