Purchasing state lottery tickets is reinforced with monetary winnings on a schedule

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.

Andy purchases only two goods, apples (a) and kumquats (k). he has an income of $125 and can buy apples at $5 per pound and kumquats at $5 per pound. his utility function is u(a, k) = 6a + 2k. what is his marginal utility for apples and his marginal utility for kumquats? andy's marginal utility for apples (mu subscript a) is mu subscript aequals 6 and his marginal utility for kumquats (mu subscript k) is

Owns a machine that can produce two specialized products. production time for product tlx is two units per hour and for product mtv is four units per hour. the machine’s capacity is 2,100 hours per year. both products are sold to a single customer who has agreed to buy all of the company’s output up to a maximum of 3,570 units of product tlx and 1,610 units of product mtv. selling prices and variable costs per unit to produce the products follow. product tlx product mtv selling price per unit $ 11.50 $ 6.90 variable costs per unit 3.45 4.14 determine the company's most profitable sales mix and the contribution margin that results from that sales mix.