Need Help On Written Optimization Analysis
drbungle
optimization_word_problem.pdf
Introduction
The state has created new legislation about “crunch-‐time”, and as such requires us to adjust our projects for the next quarter. So for the next 13 weeks we will assume that there will be no scheduled overtime. Our adjusted budget for the quarter gives us 520 hours per employee, and no overtime. So we will have to determine how many projects we can complete with these new constraints, making adjustments based on the man-‐hours worked on previous projects. Please figure out the number of game we can make of each type that yields the highest profit
Note: To convert from man-‐hours to number of people, divide the number of man-‐hours by 520 hours (which is the number of full time hours in the quarter)
Problem 1
To create a console game, we previously required 10,920 man-‐hours of development, 13,000 man-‐hours on art, 3,120 man-‐hours for design, and 2,080 man-‐hours for production management. The projected profit margin for a console game title is $1.8 million.
The work requirements for a handheld game quite a bit different: 7,280 man-‐hours in development, 2,600 man-‐hours art, 9,360man-‐hours in design, and 2,600 man-‐hours in production management. The projected profit margin for a handheld game title is $1 million.
Our current staff consists of 238 programmers, 225 artists, 180 designers, and 57 production managers. This should give us 123,760 man-‐hours in the development pool (238 x 520 = 123,760), 117,000 man-‐ hours in the art pool (225 x 520 = 117,000), 93,600 man-‐hours in the design pool (180 x 520 = 93,600), and 29,640 man-‐hours in management (57 x 520 = 29,640) to allocate to projects,
Figure out how many console and handheld games can be made this quarter to maximize our profit. In addition, report what pools (development, artists, designers, and managers) have some unutilized employees, and which pools need to be expanded.
Problem 2
We have decided to expand and create a new PC games department. Out projections indicate PC game titles will make $1.4 million in profit. The work requirements are 9,360 man-‐hours for development, 8,840 man-‐hours on artwork, 5,720 man-‐hours for design, and 1,560 man-‐hours for production management.
To help staff this department, we hired 44 more programmers for the development team, 58 more artists for the art team, and 2 more managers for the management team. Please adjust the total man-‐ hours available based on this new staff before calculating the new estimations.
Figure out how many console, PC, and handheld games can be made this quarter to maximize our profit. In addition, report what pools (development, artists, designers, and managers) have some unutilized employees, and which pools need to be expanded.
