1)The loan department in a bank will use at most $25 million or commercial and home loans. The bank's policy is to allocate at least four times as much money to home as to commercial loans. The bank's return is 12% on a home loan and 10% on a commercial loan. The manager of the loan department wants a return of at-least $2.8 million on these loans. Let x be the amount of home loans and y for the amount for commercial loans.
(a) Write a system of inequalities that describes the above conditions
(b) Graph the corresponding feasible region
2) Consider the situation of a small brewery whose ale and beer are always in demand but whose production is limited by a certain raw materials that are short in supply. Suppose the scarce ingredients are corn, hops and barely malt. To make one barrel of ale requires 5 pounds of corn, 4 ounces of hop, and 35 pounds of barley malt. To make a barrel of beer requires 15 pounds of corn, 4 ounces of hop and 20 pounds of barley malt. Suppose that 480 pounds of corn, 160 ounces of hop and 20 pounds of barley malt are available.
If each brewery of ale yields a profit of $13 and each barrel of beer yields $23 profit, how can the brewery maximize its total profit?