5.6 Solving Optimization Problems Homework !!top!!

$y = 200 - 2(50) = 100$ ft.

The 5.6 solving optimization problems homework typically involves solving optimization problems using the techniques mentioned above. Here are some examples of problems you may encounter: 5.6 Solving Optimization Problems Homework

A farmer has 200 feet of fencing to enclose a rectangular field adjacent to a long river. No fencing is needed along the river. Find the dimensions of the field that maximize the area. $y = 200 - 2(50) = 100$ ft

| Mistake | Fix | |---------|-----| | Forgetting the constraint equation | Always write it before substituting. | | Using the wrong variable to differentiate | Make sure the final function is in variable. | | Not checking domain | Sometimes $x$ can’t be negative or too large. | | Stopping at the critical point value | The problem often asks for dimensions , not just the derivative’s zero. | | Confusing max/min | Use $A''$ or a sign chart to be sure. | No fencing is needed along the river

Cost = (Area of top+bottom) × 0.03 + (Lateral area) × 0.02. ( C = 2(\pi r^2) \times 0.03 + (2\pi r h) \times 0.02 ) ( C = 0.06\pi r^2 + 0.04\pi r h )