hw1.pdf - Homework 1 Introduction to Optimization MS&E 111...

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Homework 1Introduction to OptimizationMS&E 111 / MS&E 211 / ENGR62, Stanford UniversityInstructor: Ashish GoelDue: Thursday, April 23 at 1:30pm on GradescopeSee the syllabus for submission instructions, in particular those pertaining to Excelwork. Please be sure to assign pages in your solution to the relevant problems onGradescope. The teaching staffis not responsible for grading unassigned pages.Problem 1The XYZ Corporation is undergoing a radical restructuring and needsto hire consultants to help in several key areas. XYZ has contracts with four consul-tants (A, B, C, and D). The table below indicates, for each of the consultants, whatthey charge per hour and how many hours they have available to work for XYZ.Consultantrate/hrtotal hours availableA$300/hr60B$250/hr60C$350/hr50D$200/hr40XYZ has four main tasks that need to be completed. The table below indicateshow many hours XYZ estimates that it would take each consultant to perform eachtask. If no amount of time is indicated for the consultant to complete a task, thenthe consultant cannot perform the task.Consultanthrs/task 1hrs/task 2hrs/task 3hrs/task 4A302040B303030C25252525D4040XYZ want to determine how to allocate tasks to consultants at minimum cost.Note that all tasks must be completed, but not all consultants need to be used to their

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