Needing help with a Written Optimization Setup in Finite Math

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To: Software Development Team Leaders From: Robert Hofmann Date: 12 December Re: Written Optimization Analysis M e s s a g e 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 to schedule per employee (13 weeks x 40 hours per week = 520 total hours). We have to determine how many projects we can complete during this time period, 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. Additional Information and the projected profit and estimated man-hours based on previous projects are presented in the following pages pages.

Q u a r t e r l y P r o j e c t i o n U p d a t e

Written Optimization Report: Problem 1 To create a single 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 for console game titles is $3.6 million each. The work requirements for a mobile game are 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 for handheld game titles is $2 million each. 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, Department   Console  Game   Mobile  Game   Development   10,920  man-­‐hours   7,280  man-­‐hours   Art   13,000  man-­‐hours   2,600  man-­‐hours   Management   2,080  man-­‐hours   2,600  man-­‐hours   Design   3,120  man-­‐hours   9,360  man-­‐hours  

     Profit   Projection    $3,600,000      $2,000,000    

Figure out how many console and mobile 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 could be expanded to increase profits. Note: If you want to analyze this problem in terms of number of people on each project, you will need to convert from man-hours to number of people. Divide the number of man-hours by 520 hours to determine the number of people needed to complete the work in 13 weeks.

Written Optimization Report: Problem 2 We have decided to expand and create a new PC games department. Out projections indicate PC game titles will make $2.8 million in profit each. 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. Department   Console  Game   Mobile  Game   PC  Game   Development   10,920  man-­‐hours   7,280  man-­‐hours   9,360  man-­‐hours   Art   13,000  man-­‐hours   2,600  man-­‐hours   8,840  man-­‐hours   Management   2,080  man-­‐hours   2,600  man-­‐hours   1,560  man-­‐hours   Design   3,120  man-­‐hours   9,360  man-­‐hours   5,720  man-­‐hours  

       Profit   Projection    $3,600,000      $2,000,000      $2,800,000    

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 mobile 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 could be expanded to increase profits.