Suppose rick brings 16 donuts to work and has to decide how many of the 16 to gi

Question

Suppose rick brings 16 donuts to work and has to decide how many of the 16 to give to shane and how many to give to Miriam. Assume that together they will consume all 16 donuts and ignore fractional donuts is ricks objective is to maximize the sum of the total personal use value of donuts consumed by shane and Mirium, how should he allocate the donuts?

For example, should he give 8 to each? 16 to Mirium and none to shane? Or some other combination?

Propose an allocation and write a sentence or two describing what you propose as an approach

Number of Donuts Shane's       Marginal Personal Use Value Miriam's       Marginal Personal Use Value 0 $0.00 $0.00 1 $2.00 $1.50 2 $1.90 $1.45 3 $1.80 $1.40 4 $1.70 $1.35 5 $1.60 $1.30 6 $1.50 $1.25 7 $1.40 $1.20 8 $1.30 $1.15 9 $1.20 $1.10 10 $1.10 $1.05 11 $1.00 $1.00 12 $0.90 $0.95 13 $0.80 $0.90 14 $0.70 $0.85 15 $0.60 $0.80 16 $0.50 $0.75 17 $0.40 $0.70 18 $0.30 $0.65 19 $0.20 $0.60 20 $0.10 $0.55

Explanation / Answer

The optimal quantity is when marginal personal value derived by both Shane and Miriam are equal.

This is possible when number of donuts = 11, when both have a marginal personal use value of $1.

Hence, Rick can give 11 donuts to Shane & 5 donuts to Miriam, OR 11 donuts to Miriam & 5 donuts to Shane.

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