What is the volume, in cubic centimeters, of a cylinder with a height of 5 centimeters and a base radius of 10 centimeters, to t
1 answer:
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Answer:
(a) The objective equation is and the constrain equation is
(b)
(c) The optimal values of x = 8 and y = 16
Step-by-step explanation:
Let y be the width and x the length of the rectangular garden.
(a) Determine the objective equation and the constraint equation.
- In this problem we want to maximize the area of the garden. The objective equation is the area of the rectangular garden
- The constraint is the amount of money we have for the fence and the constrain equation is
From the information given:
Cost of fence parallel to the road = $15x
Cost of the 3 other sides = $5(2y+x)
(b) Express the quantity to be maximized as a function of <em>x</em>
We use the constraint equation to solve for <em>y</em>
Substituting into the objective equation
(c) Find the optimal values of x and y
We have to figure out where the function is increasing and decreasing. Differentiating,
Next, we find the critical points of the derivative
we need to make sure that this value is the maximum using the second derivative test:
if , then f has a local maximum at
so x = 8 is a local maximum.
To find <em>y,</em>
