Answer:
A diameter of 16 inches will give the largest slice
Step-by-step explanation:
Step 1: Statement of optimization
largest slice of pizza = maximum area of the sector
Step 2: Formula for area and perimeter of sector:
Area of sector, A = 1/2r²θ
Perimeter of sector, P = 2r + rθ
Step 3: Determining the constraint
The perimeter, P, must be equal to 36 inches ie. 2r + rθ = 32
Therefore, θ = 32 -2r/r
Substituting θ in the formula for area;
A = 1/2r²(32 -2r/r)
A = -2r² + 16r
The domain of A(r) = 0 < r < 16
Step 4: Determine the maximum of object function
Critical point of A(r) , A'(r) = - 2r + 16
when A' = 0
r = -16/-2
r = 8
since, diameter, d = 2r,
Therefore, a diameter of 16 inches will give the largest slice
