5. Graphical Applications of Derivatives
Applied Optimization
1:30 minutesProblem 4.5.5a
Textbook Question
Suppose the objective function P= xy is subject to the constraint 10x + y = 100, where x and y are real numbers.
a. Eliminate the variable y from the objective function so that P is expressed as a function of one variable x.
Verified step by step guidance1
Start with the constraint equation: 10x + y = 100.
Rearrange the constraint to solve for y: y = 100 - 10x.
Substitute the expression for y into the objective function P = xy.
This gives you P = x(100 - 10x).
Now, simplify the expression to express P solely in terms of x: P = 100x - 10x^2.
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