Thursday

April 24, 2014

April 24, 2014

Posted by **Skyelar** on Monday, October 13, 2008 at 5:19pm.

1. How many of each bread should you make to maximize the profit??

2. What is the maximum profit

Would someone mind offering a guided explanation of this? I'm not sure how to set up the equations. Thank you!

- Algebra -
**Damon**, Monday, October 13, 2008 at 6:39pmThis is called "linear programming".

let i = number of Irish

let b = number of banana

then profit = p = 1.5 i + 4 b

now lets plot i on the x axis and b on the y axis. For every value of p there is a line on that graph of form:

b = (-1.5/4)i + p/4

b = -.375 i + .25 p

NOW, find the feasible region on the graph

You only have 16 flours, so there is a line going from (0,4) (8,0). Call that the flour limit line and draw it on your graph

You only have 3 sugars, so there is a line going from (0,3) to (12 ,0). Call it the sugar limit line and draw it on the graph.

the sugar line hits the flour line where?

flower line b = 4 - .5 i

sugar line b = 3 - .25 i

solve (you could get this from your graph of course)

0 = 1 -.25 i

i = 4

b = 2

NOW, we must test the corners for maximum p

corners are

(0,0)

(0,3)

(4,2)

(8,0)

p(0,0) = 0

p(0,3) = 1.5(0)+4*3 = 12

p(4,2) = 1.5*4 + 4*2 = 14

p(8,0) = 1.5(8) +4(0) = 12

so

max profit = 14 at i = 4 and b = 2

- Algebra -
**Reiny**, Monday, October 13, 2008 at 6:50pmThis is a "linear programming" problem.

Let the number of Banana bread be x

and the number of Irish bread be y

from the flour limitation we have

4x + 2y ≤ 16

2x + y ≤ 8

from the sugar limitation we have

(1/4)x + y ≤ 3

x + 4y ≤ 12

when these two are graphed in the first quadrant of a graph, we get a region bounded by the origin, the x and y intercepts closest to the origin and the intersection of the corresponding equations.

The profit equation would be

P = 4x + 1.5y

the slope of that line is -8/3

The farther this line can move away from the origin (a profit of zero) while still within our region, the larger the profit.

So we can move as far as the intersection of

2x+y = 8 and x+4y = 12

I get y = 16/7 but how can we bake 16/7 loafs of bread?

so let y be the closest whole number or y = 2, then x = 3

the profit would be 3(4) + 2(1.5) = 15

Easy Way:

since both x and y must be whole numbers, there are only 5 possible cases

(0,8), (1,6), (2,4), (3,2), and (4,0)

It would be easy to see that (3,2) produces the largest profit.

**Related Questions**

Math - Taylor plans to use 2 cups of brown sugar in making 8 loaves of whole ...

math - jeanine used 2 1/2 cups of flour to make muffins and 1 3/4 cups of flour ...

Finite Math - I keep trying to set up this problem to solve it using the Simplex...

math - this problem is given me very much difficulty because of the set up and ...

algebra - a bread recipe calls for 2/3 cup of rye flour. you only have 3/4 cup ...

Math - Here is the question: "To make a pancake mix, add 1/2 cup of sugar, 3 ...

6th grade math - I'm not sure how to solve this problem using unit rate. ...

math - You need 2b cups of flour for making b loaves of bread. You have 8 cups ...

Math - Christy had a full bag of flour. She made two batches of muffins.each ...

math - Paul is making loaves of raisin bread to sell at a fundraising event. The...