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Optimization of a Function (Answers)

Module by: Debbie Trahan. E-mail the author

Summary: This is the answer page for the Optimization of a Function Module. The student will write and graph linear functions then use these functions to write a new function using the Pythagorean Theorem. The students will then find the minimum value of the new function using a graphing calculator.

Problem

Ship A is 360 kilometers east of Shipwreck Island traveling due west toward Shipwreck Island at a speed of 15 kilometers per hour (km/hr). Ship B is 45 kilometers north of Shipwreck Island traveling due north away from Shipwreck Island at a speed of 10 km/hr.

a

A⁢t=(360−15⁢t) A t 360 15 t

B⁢t=(45+10⁢t) B t 45 10 t

Figure 1
Figure 1 (optans1c.jpg)

b

A⁢10=210 A 10 210

B⁢10=145 B 10 145

The distance between Ship A and Ship B after 10 hours is 210 2 +145 2 =65125≃255.196 km 210 2 145 2 65125 255.196 km

c

A⁢16=120 km A 16 120 km

B⁢16=205 km B 16 205 km

Ship B is 205 km from Shipwreck Island when Ship A is 120 km.

d

Ship A and Ship B are 171 km from Shipwreck Island after 12.6 hours.

e

A⁢24=0 A 24 0

B⁢24=285 B 24 285

Ship B is 285 km from Shipwreck Island when Ship A reaches Shipwreck Island.

f

d⁢t=360−15⁢t2+45+10⁢t2 d t 360 15 t 2 45 10 t 2

g

Figure 2:
Figure 2 (optans3.png)
Figure 3
Figure 3 (optans2.png)

At approximately 15.230 hours, the distance between Ship A and Ship B is the least. The distance at this time is approximately 237.134 km.

Link to Student Page

To view the Optimization of Functions Student Page, click on the link below.

Go to Student Page

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