lecture29hout

# lecture29hout - MATH 006 Calculus and Linear...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 29) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 14 Outline 1 Optimization Albert Ku (HKUST) MATH 006 2 / 14 Optimization Optimization Problems Strategy for solving optimization problems: Step 1: Introduce variables, look for relationships among the variables, and construct a mathematical model of the form Maximize (or minimize) f ( x ) on the interval I . Step 2: Find the critical value(s) of f ( x ). Step 3: Find the absolute maximum (or minimize) value of f ( x ) on the interval I and the value(s) of x where this occurs. Step 4: Use the solution to the mathematical model to answer all the questions asked in the problem. Albert Ku (HKUST) MATH 006 3 / 14 Optimization Example 1 Example A homeowner has \$320 to spend on building a fence around a rectangular garden. Three sides of the fence will be constructed with wire fencing at a cost of \$2 per linear foot. The fourth side is to be constructed with wood fencing at a cost of \$6 per linear foot. Find the dimensions and the area of the largest garden that can be enclosed with \$320 worth of fencing. Solution Let x and y be the lengths of the fence as shown in the following figure: Albert Ku (HKUST) MATH 006 4 / 14 Optimization Solution (cont’d) Since the total cost of the fence C is \$320, we have C = 2 y + 2 x + 2 y + 6 x = 8 x + 4 y = 320 ⇒ y = 80- 2 x Now, we need to maximize the area of the garden, denoted by...
View Full Document

{[ snackBarMessage ]}

### Page1 / 14

lecture29hout - MATH 006 Calculus and Linear...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online