Answer to Question #8696 in Differential Equations for sami

Question

Jamal has been an idea for a new computer game that they want to develop. The function T (x) = 100-20x + 2 x → 2 discloses the time in days it takes for the x programmers to develop the game.
a) How many programmers should be set aside for uppgigten if you want the game finished in the shortest possible time?
b) How many days are needed to get the game completed in the shortest possible time?

Answer 1

To find the number of programmes which minimisers time we should find derivative of T(x):
T'(x)=-20+4x
and find its zero points:
-20+4x=0 => x=5
To show that it's really a maximum point we find second derivative T''(x)=4>0 so we found maximu& point
x=5 is the number of programmers to finiksh the game in teh shortest time. To find this very time in days we calculate T(5)=100-20*5+2*25=50 days