Upcoming SlideShare
×

# Alg2 lesson 3-4

314 views
278 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
314
On SlideShare
0
From Embeds
0
Number of Embeds
33
Actions
Shares
0
0
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Alg2 lesson 3-4

1. 1. (1, 2) (1, 4) (5, 8) (5, 2) Maximum value = 11 at (5,2) Minimum value = -5 at (1, 4) x y 3x – 2y 1 2 3(1)-2(2) = -1 5 2 3(5)-2(2) = 11 5 8 3(5)-2(8) = -1 1 4 3(1)-2(4) = -5
2. 2. What do you need to make a paper airplane? Paper Money (to buy the paper) Time Resources
3. 3. Emily sells prom dresses that she makes herself. For each basic dress she sells, she earns a profit of \$20, and each deluxe dress she sells earns a profit of \$35. To make each basic dress, she must use 2 yards of cotton fabric and 2 yards of silk; each deluxe dress requires 3 yards of cotton and 1 yard of silk. She has purchased a total of 180 yards of cotton fabric and 100 yards of silk. Determine the number of basic dresses and the number of deluxe dresses she must sell to maximize her profit. Resources: Cotton Fabric Silk Fabric
4. 4. Emily sells prom dresses that she makes herself. For each basic dress she sells, she earns a profit of \$20, and each deluxe dress she sells earns a profit of \$35. To make each basic dress, she must use 2 yards of cotton fabric and 2 yards of silk; each deluxe dress requires 3 yards of cotton and 1 yard of silk. She has purchased a total of 180 yards of cotton fabric and 100 yards of silk. Determine the number of basic dresses and the number of deluxe dresses she must sell to maximize her profit. Variables: number of Basic dresses number of Deluxe dresses B D
5. 5. Emily sells prom dresses that she makes herself. For each basic dress she sells, she earns a profit of \$20, and each deluxe dress she sells earns a profit of \$35. To make each basic dress, she must use 2 yards of cotton fabric and 2 yards of silk; each deluxe dress requires 3 yards of cotton and 1 yard of silk. She has purchased a total of 180 yards of cotton fabric and 100 yards of silk. Determine the number of basic dresses and the number of deluxe dresses she must sell to maximize her profit. Objective function: 20B + 35D
6. 6. To make each basic dress, she must use 2 yards of cotton fabric and 2 yards of silk; each deluxe dress requires 3 yards of cotton and 1 yard of silk. She has purchased a total of 180 yards of cotton fabric and 100 yards of silk. Constraints Variables Basic Dresses Deluxe Dresses Total Resources Cotton Silk
7. 7. To make each basic dress, she must use 2 yards of cotton fabric and 2 yards of silk; each deluxe dress requires 3 yards of cotton and 1 yard of silk. She has purchased a total of 180 yards of cotton fabric and 100 yards of silk. Constraints 180 100 2 2 3 1 B B D D 2B + 3D  180 2B + D  100 B ≥ 0 D ≥ 0 Variables Basic Dresses Deluxe Dresses Total Resources Cotton Silk
8. 8. 2B + 3D  180 2B + D  100 B ≥ 0 D ≥ 0 20 40 60 80 100 Basic dresses Deluxe dresses 100 80 60 40 20 (0,100) (90, 0) (50, 0) (0, 60) Vertices: (0, 60) (50, 0) (0, 0) (30, 40)
9. 9. Values of vertices in objective function (0, 60) (50, 0) (0, 0) (30, 40) 20B + 35D (B, D) 20(0) + 35(60) = 2100 20(50) + 35(0) = 1000 20(0) + 35(0) = 0 20(30) + 35(40) = 2000 Determine the number of basic dresses and the number of deluxe dresses she must sell to maximize her profit. Sell 0 Basic and 60 Deluxe Dresses for a maximum profit of \$2100
10. 10. (-5,-2) (3, 2) (1,-2) Maximum value = 10 at (3,2) Minimum value = -18 at (-5, -2) x y 4x – y 3 2 4(3)-(2) = 10 1 -2 4(1)-(-2) = 6 -5 -2 4(-5)-(-2) = -18