3. Problem Solving
Optimization Basics — Quiz
Test your understanding of optimization basics with 5 practice questions.
Practice Questions
Question 1
A rectangular field is to be enclosed by $200$ meters of fencing. One side of the field is along a river and does not need fencing. What is the maximum area of the field?
Question 2
A company produces $x$ units of a product. The total cost $C(x)$ is given by $C(x) = 0.5x^2 - 10x + 500$. What is the number of units that should be produced to minimize the total cost?
Question 3
An open-top cylindrical tank is to be constructed with a volume of $1000\pi$ cubic feet. If the radius of the base is $r$ and the height is $h$, what is the expression for the surface area $A$ of the tank in terms of $r$ only?
Question 4
A projectile is launched vertically upwards. Its height $h(t)$ in meters after $t$ seconds is given by $h(t) = -4.9t^2 + 98t + 5$. At what time $t$ does the projectile reach its maximum height?
Question 5
A rectangular box with a square base and an open top has a volume of $32$ cubic feet. What is the minimum surface area of the box?