Question

A small company produces two goods, swords and plowshares. The company has 100 type alpha employees and 100 type beta employees. If an alpha devotes all his time to producing swords, he can make 2 swords per week. If he devotes all his time to producing plowshares, he can make 4 plowshares per week. A beta can produce either 1 plowshare per week or 1 sword per week. The company wants to produce 218 swords and as many plowshares as it can. How many type betas should it employ at making swords?

a.	100
b.	18
c.	90
d.	0
e.	None of the above.

Answer 1

Solution :-

Given :-

Alpha can produce either 2 swords or 4 plowshares.

Therefore to produce 2 sword Alpha sacrifice 4 plowshares.

Thus in order to produce 1 sword he has to sacrifice 2 plowshares.

Hence opportunity cost of producing 1 sword for Alpha = 2 plowshares.

Given :-

Beta can produce either 1 swords or 1 plowshares.

Therefore to produce 1 sword Beta sacrifice 1 plowshare.

Hence opportunity cost of producing 1 sword for Beta = 1 plowshares.

Opportunity cost of producing sword for Beta is less than opportunity cost of producing sword for Alpha.

Hence Beta should specialize in Producing swords and used all its time in producing swords.

Here Target is 218 swords and as many plowshares as it can.

Hence As discussed above, Beta specialize in Producing swords and used all its time in producing swords.

Now Company has 100 Beta

So Company can employ all Beta = 100

Therefore Correct Answer is (A)

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