A "mathematically fair bet" is one in which a gambler bets, say, $100 for a 10 percent chance to win $1,000 ($100 = 0.10× $1,000).
a. Assuming diminishing marginal utility of dollars, this isnota fair bet in terms of utility because
b. When the "house" takes a cut of each dollar bet, the bet is .

Cereal type 1 sells for $1.50/kg. it should contain at least 22% protein, 2% of minerals and vitamins, and at most 30% of starch by weight. cereal type 2 sells for $1.00/kg. it should contain at least 30% starch by weight. what is the optimal product mix for the company?

Maldonia has a comparative advantage in the production of , while lamponia has a comparative advantage in the production of . suppose that maldonia and lamponia specialize in the production of the goods in which each has a comparative advantage. after specialization, the two countries can produce a total of million pounds of lemons and million pounds of coffee.

Alarge tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.