Rancher Esther raises cattle and hogs. Some of her facilities are better suited for cattle and some are better suited fo

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Rancher Esther raises cattle and hogs. Some of her facilities
are better suited for cattle and some are better suited for
hogs—but all facilities can be used to raise either. Esther has
been able to total all of the costs of raising either type of
animal, and has recognized that the costs depend on the mix of
cattle and hogs being raised on the ranch. Specifically, Esther
finds that if 1% of her animals are cattle, the cost per pound of
raising the cattle is 101% of the cost of raising a pound of hog.
If 2% of her animals are cattle, the cost per pound of raising the
cattle is 102% of the cost of raising a pound of hog, and so forth.
For example, if 99% of the animals are cattle, the cost per pound
of raising the cattle is 199% of the cost of raising a pound of
hog. Esther always finds that it is best to keep her ranch filled
to capacity with animals.
Ignoring all other issues, what mix of cattle and hogs (in
percentages) should Esther raise if the market price for live
cattle per pound is 40% higher than the market price for live hogs
per pound? (Enter your answer as a whole number.)