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Sagot :
Answer:
A. 4x + h
B. 4x + h = 78
V = x²h
Step-by-step explanation:
1. The length plus girth
X +x+x+x +h
= 4x +h
2. Constraint equation
4x + h = 78 ----(1)
Objective function
Volume = v = x*x*h
V = x²h ----(2)
3. Quantity as function of x
From equation 1 in answer part b
4x+h = 78
We make h subject
h = 78-4x
We put values of h in equation 2 in part b
V = x²h
V = x²(78-4x)
V = 78x²-4x³
To get values of x and h
V = 78x²-4x³
Dv/dx = 0
= 156x - 12x²
156x = 12x²
Divide through by 12x
156x/12x = 12x²/12x
x = 13
h = 78-4x
h = 78 - 4(13)
h = 78 - 52
h = 26 inches

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