1. Using MS Excel for LP Collect homework Roll Call Review homework
Lecture: Using MS Excel’s Solver
Small Group Exercise
Lecture: More Excel
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2. #9: The Brewery
The brewery produces beer and ale. Beer sells for $5 per barrel, and ale for $2/barrel. Producing a barrel of beer requires 5 pounds of corn and 2 pounds of hops. Producing a barrel of ale requires 2 pounds of corn and 1 pound of hops. The brewery has 60 pounds of corn and 25 pounds of hops.

3. #9: The Brewery

4. #9: The Brewery Max Z ( revenue ) = 5 x1 + 2 x2
S. T. 5 x1 + 2 x2 <= 60
2 x1 + 1 x2 <= 25
x1, x2 >= 0

5. #9: The Brewery Max Z ( revenue ) = 5 x1 + 2 x230 25
Max Z ( revenue ) = 5 x1 + 2 x2
S. T. 5 x1 + 2 x2 <= 60
2 x1 + 1 x2 <= 25
x1, x2 >= 0
0, 25 = $50
10, 5 = $60 3
12, 0 = $60 3 12
,12.5

6. #10: The Baker
A gourmet cook bakes two types of cake, chocolate and vanilla, to supplement her income. Each chocolate cake can be sold for $12, and each vanilla cake can be sold for $9. Each chocolate cake requires 20 minutes of baking time and uses 4 eggs. Each vanilla cake requires 40 minutes of baking time and uses 1 egg. The baker has 8 hours of baking time and 30 eggs.

7. #10: The Baker

8. #10: The Baker Max Z ( profit ) = 12 x1 + 9 x2
S. T. 20 x x2 <= 480
4 x1 + 1 x2 <= 30
x1, x2 >= 0, integers

9. #10: The Baker 30
To find a point’s coordinates that aren’t obvious, solve simultaneous equations.
0,12
??, ?? 12
7.5,0 3 3
7.5 24

10. #10: The Baker 30
20 x x2 <= 480
-5(4) x (1) x2 <= -5 (30)
0,12
??, ?? 12
7.5,0 3 3
7.5 24

11. #10: The Baker 20 x1 + 40 x2 = 480 -20 x1 - 5 x2 = -150 0 35 x2 = 330
x2 = 330/35 or
= 66/7
0,12
??, ?? 12
7.5,0 3 3
7.5 24

12. #10: The Baker 30
Isoprofit lines: Solve the optimization equation for x2 to find the slope of the profit line.
0,12
36/7, 66/7 12
7.5,0 3 3
7.5 24

13. #10: The Baker Z = 12 x1 + 9 x2 Z - 12 x1 = 9 x2 Z/9 - 12/9 x1 = x2
5, 9 = $141

14. 11. Woodco
...tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 150 board feet of oak and 210 board feet of pine are available. A table requires either 17 board feet of oak or 30 board feet of pine. A chair requires either 5 board feet of oak or 13 board feet of pine. Each table sells for $40, and each chair for $15.

15. #11: Woodco

16. #11: Woodco Max Z ( profit ) = 40 x1 + 15 x2
S. T. 17 x x2 <= 150
30x x2 <= 210
x1, x2 >= 0, integers

17. WRONG - FOLLOW ME #11: Woodco Max Z ( profit ) = 40 x1 + 15 x2
S. T. 17 x x2 <= 150
30x x2 <= 210
x1, x2 >= 0, integers
WRONG - FOLLOW ME
0, 210/13 =
~$240
7, 0 = $280

18. Using MS Excel’s Solver
EX: using the Woodco example.
Create the table of information.
Set up formulas to relate the information to be optimized.
Set up solver to list constraints.
Run solver.

19. Go to MS Excel w/ 9-3cexblank

20. EX: Chicken Feed
A farmer feeds chickens, maintaining a particular level of nutrition. Minimize the cost, using this information: