Optimization Problems - Grade 9 Math
This worksheet focuses on solving optimization problems by finding maximum or minimum values of functions in various contexts.
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Standards
Optimization Problems
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Read each problem carefully and solve for the optimal solution. Show all your work.
1. A farmer has 400 meters of fencing and wants to build a rectangular enclosure for his sheep. What are the dimensions of the rectangle that will maximize the area?
2. A company wants to design a cylindrical can with a volume of 1000 cm³. What dimensions (radius and height) will minimize the amount of material needed to construct the can?
3. To find the maximum or minimum value of a function, we typically use to find the critical points.
4. An optimization problem involves finding the or value of a quantity.
5. Which of the following is a common step in solving optimization problems?
Guessing the answer
Setting the derivative to zero
Ignoring constraints
Using only algebraic methods
6. All optimization problems have a unique solution.
True
False
7. A company sells a product for $100 per unit. The cost of producing x units is given by C(x) = 50x + 500. The demand function is P(x) = 150 - 0.5x. Find the number of units that should be produced and sold to maximize revenue.