IEOR 153: Spring 2020
Problem Set 5
Instructor: Matt Olfat
Issued: 4/20/20 Due: 5/1/20
Problem 1: 20 points
The government would like to allocate loans to small businesses for use towards payroll. The loans
are structured such that they are highly beneficial if used for payroll for existing employees and
not so beneficial if used otherwise, so the ideal scenario for each company is to receive exactly
the exactly the cost of its employees’ wages and benefits for the month (i.e. each marginal dollar
received below this amount comes with opportunity cost, and each marginal dollar received over
this amount will incur a future cost due to high interest rates). Assume that each company knows
this value, and denote it as vi for company i. Also, assume that there are n companies vying for
these loans. The government has K dollars to allocate, with K < Pn i=1 vi. All companies are
asked to submit a value, bi, representing thei
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