# Quanitive Methods

posted by .

A car rental company has \$540,000 to purchase up to 25 new cars of two different models. One model costs \$18,000 each and the other model costs \$24,000 each. Write a system of linear inequalities to describe the situation. Let x represent the first model and y represent the second. Find the region described by the system of linear inequalities.

• Quanitive Methods -

Well, you know that you have 540,000 dollars to spend, so model x*18,000 + y*24,000 < 540,000.

Next, you know that at most, you may buy 25 new cars, so x + y < 25.

If you treat these two inequalities as equations, you can solve for the extreme points. That is say:
x+y = 25 so
y = 25 - x. Plug y into the first equation and you get 540,000 = x*18,000 + (25-x)*24,000.
Solve for x:
540 = 18x + 600 - 24x
-60 = -6x
x = 10
plug in x=10 into x+y = 25 and you get:
10 + y = 25
y = 15
So, if you buy 10 x model, and 15 y model cars, you'll spend all your money, and have the most cars possible. However, remember that these were inequalities. There is nothing stopping you from spending all your money on model x, or all of it on model y. Also, nothing says that you have to spend all your money either. If you spent all your money on model x, you would get 540,000 / 18,000 = 30 of those. If you spent it all on model y, you would get 22.5 of them. To show the region described by the system, I would make a two sided graph that looks like this:
|. |
| - .|
|_________| The left vertical line is model x, the right is model y. Going across the bottom is increasing model x and decreasing model y. The y-intercept on the left axis is 30, and the y-intercept on the right axis is 22.5. Where the two cross in the middle is where you get the most car for your money.

Best of luck!

• Quanitive Methods -

Sorry, the formatting on the graph got messed up. It should be a horizontal line with two vertical lines sticking up at each end.

## Similar Questions

1. ### probability

2.The daily production from a car factory=3 different models-A,B,C which are in two different colours-R and S. Daily the factory produces 1600 model A cars,800 of model B and 600 of model C. Overall,40% of the cars are of colour R,60% …
2. ### accounting

"Harris Company manufactures and sells a single product. A partically completed schedule of the company's total and per unit cost over the relevant range of 30,000 to 50,000 per units produced and sold are: United produced and Sold: …
3. ### Economics

The accompanying table shows a car manufacturerâ€™s total cost of producing cars: Qty |TC| Variable Costs| Avg. Var. Costs| Avg. Total Costs| Avg. Fixed Costs 0 |\$500,000| ---- | ---- | ---- |---- | 1 |540,000 | 2 |560,000 | 3 |570,000 …
4. ### Fin/571

3. Bell Mountain Vineyards is considering updating its current manual accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the system continues to decline. The …
5. ### statistics

In this question, use Excel functions rather than Normal distribution tables. The number of new cars sold by "Ma's New Car Factory" in a financial year can be approximated by a normal distribution with a mean of 125,000 cars and a …
6. ### Math

2)Jenny wants to buy a new car, and she has narrowed her choices to two models. Model A sells for \$12,500, gets 25mi/gal, and costs \$300 a year for insurance Model B sells for \$16,100, gets 36 mi/gal, and costs \$400 a year for insurance. …
7. ### Accounting

Mushroom Company, a retail company, has two departments, "G" and "S". The company's most recent monthly contribution format income statement is presented below. ...................................Total..................................G...............................S …
8. ### Math

Ben wants to buy a new car, and she has narrowed her choices to two models. Model A sells for \$12,500, gets 25mi/gal, and costs \$300 a year for insurance Model B sells for \$16,100, gets 36 mi/gal, and costs \$400 a year for insurance. …
9. ### Math

Ben wants to buy a new car, and she has narrowed her choices to two models. Model A sells for \$12,500, gets 25mi/gal, and costs \$300 a year for insurance Model B sells for \$16,100, gets 36 mi/gal, and costs \$400 a year for insurance. …
10. ### math

A clothing company has budgeted \$58,000 for the purchase of 7 sewing machines. The 7 sewing machines are to be chosen from two models, model X and model Y. If a model X sewing machine costs \$8,000 and a model Y sewing machine costs …

More Similar Questions