Quote:
Originally Posted by HelpxMe
Hey all, I need help on this last question.. Its due tomorrow at 11:59pm and I don't understand how to complete this problem!! HELP PLEASE..
Problem 2
We have decided to expand and create a new PC games department. Out projection indicate a PC game makes 40% more profit; that is, about $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.
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.

I used some of my answer to problem 1 for this problem.
d = development
a = art
s = design
p = production
Console (c= number of consoles)

d: 10920/520 = 21 people
a: 13000/520 = 25 people
s: 3120/520 = 6 people
p: 2080/520 = 4 people
Handheld (h = number of handhelds)

d: 7280/520 = 14 people
a: 2600/520 = 5 people
s: 9360/520 = 18 people
p: 2600/520 = 5 people
PC (p = number of PCs)

d: 9360/520 = 18 people
a: 8840/520 = 17 people
s: 5720/520 = 11 people
p: 1560/520 = 3 people
After adding the additional workers we now have:
238 + 44 = 282 programmers for development
225 + 58 = 283 artists
180 designers
57 + 2 = 59 managers for production
So our limits are given by:
Eq. 1: 21c + 14h + 18p <= 282
Eq. 2: 25c + 5h + 17p <= 283
Eq. 3: 6c + 18h + 11p <= 180
Eq. 4: 4c + 5h + 3p <= 59
Now we have 4 equations with three variables. We have to use combinations of 4 equations taken three at a time (4 combinations) to find the vertices. Using an online matrix calculator to solve systems of 3 simultaneous equations gives:
Eq.1, Eq. 2, Eq. 3: c = 29.835, h = 20.774, p = 66.632
Eq.1, Eq. 2, Eq. 4: c = 8, h = 3, p = 4
Eq.1, Eq. 3, Eq. 4: c = 4.048, h = 3.741, p = 8.034
Eq.2, Eq. 3, Eq. 4: c = 4.092, h = 2.609, p = 9.862
We can ignore the results of Eq.1, 2, and 3 because we get negative values for c, and h.
Plugging the other results into our profit equation and looking for the maximum gives:
Profit = 1.8c + 1h + 1.4p
Since we cannot make fractions of a console, handheld, or pc game then round the values to give:
Profit = 1.8(8) + 1(3) + 1.4(4) = 23 million dollars
Profit = 1.8(4) + 1(3) + 1.4(8) = 21.4 million dollars
Profit = 1.8(4) + 1(2) + 1.4(9) = 21.8 million dollars
So max profit comes from making 8 consoles, 3 handhelds, and 4 pc games.