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Please help me with this question

This is a question on opportunity cost. I had problem in solving the last part. Please help me out.

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2 Answers 2

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Consider this allocation:

Apple: $55$ hours on Phones, $15$ hours on Tablets.

Samsung: All $70$ hours on Tablets.

I leave it as an excercise for you to check it works.

Initially what I thought was having each company produce what they're most efficient in, then change it and have Apple produce one Tablet more until it worked, as initially the Tablets were falling short.

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For part three Apple can allocate anywhere from (17.5, 35] labor units for phones, with the rest going to tablets. Samsung can allocate (7, 14] to phones, with the rest going to tablets.

This is because, with both companies, it's cheaper to produce more phones than it is tablets, therefore increasing the total production. This can be further observed when plotting out 2x + 5y = 70 for Apple, and 5x + 7y = 70 for Samsung (x's representing phones, y's representing tablets). Since the question calls for maximizing x + y and the absolute value of the slope is less than one (gaining more phones than losing tablets), we can have greater total production by simply increasing the labor units put into phones to any amount.

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