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kolezko [41]
2 years ago
12

Suppose that a worker in Freedonia can produce either 6 units of corn or 2 units of wheat per year, and a worker in Sylvania can

produce either 2 units of corn or 6 units of wheat per year. Each nation has 10 workers. Without trade, Freedonia produces and consumes 30 units of corn and 10 units of wheat per year. Sylvania produces and consumes 10 units of corn and 30 units of wheat. Suppose that trade is then initiated between the two countries, and Freedonia sends 30 units of corn to Sylvania in exchange for 30 units of wheat. Freedonia will now be able to consume a maximum of:________
a. 30 units of corn and 30 units of wheat.
b. 40 units of corn and 30 units of wheat.
c. 40 units of corn and 20 units of wheat.
d. 10 units of corn and 40 units of wheat.
Business
1 answer:
Svetradugi [14.3K]2 years ago
3 0

Answer:

a. 30 units of corn and 30 units of wheat.

Explanation:

In a two-product, two-country world, international trade leads to specialization. Each country will produce the product in which it has comparative advantage. In this case, Freedonia will produce only corn and Sylvania will produce only wheat. With all constant, the country will consume the same amount of that product, but the surplus will exchange it for the other product. Freedonia will use all its workers to produce corn, in a year they will produce 6*10= 60 units of corn. Sylvania will use the 10 workers to produce wheat, in a year they will produce 6*10=60 units of wheat.

But, Freedonia will consume the same amount of corn (30 units). Then, Freedonia have 30 available units to trade with Sylvania. And the same for Sylvania, they will consume the same amount of wheat (30 units) and so Sylvania will have 30 available units of wheat to trade with Freedonia.

If the price, for both goods, is the same, Ricardo´s theory predicts that total consumption in both countries will increase, then consumer welfare will increase. Freedonia will consume the same 30 units of corn, but the other 30 will be exchanged by 30 units of wheat. Consumers are better and happier. Freedonia will consume 20 units more of wheat than before without sacrifying units of corn.

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Each machine must be run by one of 19 cross-trained workers who are each available 35 hours per week. The plant has 10 type 1 ma
Mrac [35]

Answer:

The Linear programming model is given as below

Profit Function: P=90X+120Y+150Z

Constraints:

2X+2Y+Z\leq 400

3X+4Y+6Z\leq 240

4X+6Y+5Z\leq 320

\dfrac{2X+2Y+Z}{40}\leq 10

\dfrac{3X+4Y+6Z}{40}\leq 6

\dfrac{4X+6Y+5Z}{40}\leq 8

\dfrac{2X+2Y+Z}{35}+\dfrac{3X+4Y+6Z}{35}+\dfrac{4X+6Y+5Z}{35}\leq 19

Explanation:

As the question is not complete, the complete question is found online and is attached herewith.

Let the number of product 1 to be produced is X, that of product 2 is Y and product 3 is Z

so  the maximizing function is the profit function which is given as

P=90X+120Y+150Z

Now as the number of hours in a week are 40 and there are a total of 10 type 1 machines so the total number of machine 1 hours are 40*10=400 hours

As from the given table product 1 uses 2 machine hours of machine 1, product 2 uses 2 machine hours of machine 1 and product 3 uses 1 hour of machine 1 so

2X+2Y+Z\leq 400

Now as the number of hours in a week are 40 and there are a total of 6 type 2 machines so the total number of machine 2 hours are 40*6=240 hours

As from the given table product 1 uses 3 machine hours of machine 2, product 2 uses 4 machine hours of machine 2 and product 3 uses 6 hour of machine 2 so

3X+4Y+6Z\leq 240

Now as the number of hours in a week are 40 and there are a total of 8 type 3 machines so the total number of machine 3 hours are 40*8=320 hours

As from the given table product 1 uses 4 machine hours of machine 3, product 2 uses 6 machine hours of machine 3 and product 3 uses 5 hour of machine 3 so

4X+6Y+5Z\leq 320

Now as the machine 1 is used as 2X+2Y+Z in a week and the week is of 40 hours so the number of machines to be used are given as

\dfrac{2X+2Y+Z}{40}\leq 10

Now as the machine 2 is used as 3X+4Y+6Z in a week and the week is of 40 hours so the number of machines to be used are given as

\dfrac{3X+4Y+6Z}{40}\leq 6

Now as the machine 3 is used as 4X+6Y+5Z in a week and the week is of 40 hours so the number of machines to be used are given as

\dfrac{4X+6Y+5Z}{40}\leq 8

Now the workers are available for 35 hours so the worker available at the machine 1 is given as

\dfrac{2X+2Y+Z}{35}

That of machine 2 is given as

\dfrac{3X+4Y+6Z}{35}

That of machine 3 is given as

\dfrac{4X+6Y+5Z}{35}

As the total number of workers is 19 so the constraint is given as

\dfrac{2X+2Y+Z}{35}+\dfrac{3X+4Y+6Z}{35}+\dfrac{4X+6Y+5Z}{35}\leq 19

So the Linear programming model is given as below

Profit Function: P=90X+120Y+150Z

Constraints:

2X+2Y+Z\leq 400

3X+4Y+6Z\leq 240

4X+6Y+5Z\leq 320

\dfrac{2X+2Y+Z}{40}\leq 10

\dfrac{3X+4Y+6Z}{40}\leq 6

\dfrac{4X+6Y+5Z}{40}\leq 8

\dfrac{2X+2Y+Z}{35}+\dfrac{3X+4Y+6Z}{35}+\dfrac{4X+6Y+5Z}{35}\leq 19

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2 years ago
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