Total cost, C = 8x^2 + 12xz
volume, V = (x^2)*z = 10
C = 8x^2 + 12x*10/x^2
= 8x^2 + 120/x
dC/dx = 16x - 120/x^2 = 0
16x = 120/x^2
x^3 = 120/16
x = 1.957 ft
d^2C/dx^2 = 16 +240/x^3 = +ve for x = 1.957
so, C is minimum when
x = 1.957 ft z = 2.61 ft
Length of the base x is 1.957 ft and height of side z is 2.61 ft
Volume is length x width x height.
Calculate the volume of each rectangle and add them together.
7.5 x 7.5 x 3.55 = 199.6875
7.5 x 3.55 x 3.55 = 94.51875
Volume = 94.51875 + 199.6875 = 294.21 cubic meters
312.5/x=100/12.8
<span>(312.5/x)*x=(100/12.8)*x </span>
<span>312.5=7.8125*x </span>
<span>312.5/7.8125=x </span>
<span>40=x </span>
<span>x=40</span>
<span>3 < -5n + 2n
Add 2n to -5n
3<-3n
Divide -3 on both sides while flipping the inequaltiy sign.
Final Answer: -1>n</span>
