# Math Help - Graphical Method Word Problems

1. ## Graphical Method Word Problems

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?

2. ## Re: Graphical Method Word Problems

Originally Posted by NateDawg
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 items as much money to home as to commercial loans. I don't understand this. What "four items"? Do you mean "four times as much money"? I'm going to assume that. 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
"The bank's policy is to allocate at least four times as much money to home as to commercial loans." So $x\ge 4y$.
"The manager of the loan department wants a return of at-least $2.8 million on these loans." I assume this is "per year". The return on loans of x dollars at 12% interest is .12x. The return on loans of y dollars at 10% interest is .10y. The total is $.12x+ .10y\ge 2800000$ (b) Graph the corresponding feasible region You also have, of course, $x\ge 0$ and $y\ge 0$. To find the boundary of the feasible region replace each inequality sign by and equals sign and graph the resulting line. 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 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?
You seem to have left out important information- "To make one barrel of ale requires 5 pounds of corn, 4 ounces of hop, and 20 pounds of barley malt" but how much is required to make a barrel of beer?

3. ## Re: Graphical Method Word Problems

Edited to reflect corrections