My textbook had this question: 50 identical families are living in city A. They

Question

My textbook had this question:

50 identical families are living in city A. They make each hour either one loaf of bread or one shirt.

Jim enters the town and makes a factory, which is employed by the locals. Every worker in the factory works on one machine and is able to produce 6 shirts per hour. The cost of running the machine is half a loaf of bread per hour, the cost to employ each worker is 1.5 loaves of bread per hour.

The customers of the factory are the families of city A.

The time it takes to travel back and forth to the factory is 5 minutes per kilometer. For example, someone who is 2 kilometers away from the factory will lose 10 minutes to make the trip back and forth to the factory.

Which of the families in the city will buy their shirts from the factory rather than make them themselves?

The answer given in the book is only those who live within 8 kilometers from the factory. I don't understand how they arrived at this answer. Please explain. Thank you.

Explanation / Answer

cost of making 6 shirts by machine = 2 loaves of bread so cost for 1 shirt = 2/6 = 1/3 loaf of bread. If x is the distance to be travelled by a family to buy shirt from the factory, time taken = 5*2x minutes= x/6 hour (for up and down travel.) the family loses x/6 loaf of bread which otherwise he could have been made. 1/3 loaf is to be paid as cost and 1 shirt is = 1 loaf for family so total cost = 1+ 1/3 = 4/3 loaves loss of time < = gain in value of shirt so, x/6 x

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