Help! Baker's Dozen Inequality Problem

[bristar101]

Mr. and Mrs. Baker have a small bakery that specializes in doughnuts. The make only two kinds of doughnuts -plain and icing. They need to decide how many dozens of each kind of doughnut to make for tomorrow.

1 dozen of their plain requires 1 lb. of dough(no icing), while one dozen of their icing doughnuts requires .75 lb. of dough and .4 lb of icing.

They know that the plain doughnuts require .1 hour of preparation, and each icing one takes .15 hours.of preparation. They also know that no matter how many they make, they'll sell it all.

Their decision is limited by the following:
-They have 110lb of dough and 32lb of icing (ingredients)
-they have room for a total of 140 dozen doughnuts (oven space)
-They only have 15 hours of preparation time (preparation time)

They want to make the most money as possible. They sell plain for $6.00 and it cost them $4.50 (per dozen). The iced doughnuts sell for $7.00 and cost $5.00 a dozen to make. How many dozens so each kind of doughnuts should Mr. and Mrs. Baker make so that their profit is as high as possible?

- I need inequalities for these (so I could graph them) Also, how would I find maximum profit?

I have tried hard to figure this out, I got some inequalities but I have no idea if they are correct.
Thanks!

 

[Deleted member 4993]

Mr. and Mrs. Baker have a small bakery that specializes in doughnuts. The make only two kinds of doughnuts -plain and icing. They need to decide how many dozens of each kind of doughnut to make for tomorrow.

1 dozen of their plain requires 1 lb. of dough(no icing), while one dozen of their icing doughnuts requires .75 lb. of dough and .4 lb of icing.

They know that the plain doughnuts require .1 hour of preparation, and each icing one takes .15 hours.of preparation. They also know that no matter how many they make, they'll sell it all.

Their decision is limited by the following:
-They have 110lb of dough and 32lb of icing (ingredients)
-they have room for a total of 140 dozen doughnuts (oven space)
-They only have 15 hours of preparation time (preparation time)

They want to make the most money as possible. They sell plain for $6.00 and it cost them $4.50 (per dozen). The iced doughnuts sell for $7.00 and cost $5.00 a dozen to make. How many dozens so each kind of doughnuts should Mr. and Mrs. Baker make so that their profit is as high as possible?

- I need inequalities for these (so I could graph them) Also, how would I find maximum profit?

I have tried hard to figure this out, I got some inequalities but I have no idea if they are correct.
Thanks!

Since you have tried some steps - please share those with us - even if you think those are incorrect

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[bristar101]

What I have and what I need specifically

For preparation time I got: P≤-1.5I +150
Oven Space: P≤-1.5+140
Dough: P≤110
Icing: I≤80

*P= Plain doughnuts
I= Iced doughnuts

-Would these inequalities represent the situation? I'm not sure.
- How would I use this(and after graphing) and the info in the problem to find maximum profit?

 

[HallsofIvy]

For preparation time I got: P≤-1.5I +150
Oven Space: P≤-1.5+140
Dough: P≤110
Icing: I≤80

*P= Plain doughnuts
I= Iced doughnuts

-Would these inequalities represent the situation? I'm not sure.
- How would I use this(and after graphing) and the info in the problem to find maximum profit?

Draw the lines representing the corresponding equality on coordinate system. The region satisfying the inequality is one side of that line. To see which line put P= I= 0 into each. The inequality is satisfied so the correct side is the one with (0, 0) on it.

If you are given a problem like this, I presume you have learned the basic rule of "linear programming"- that the max or min of a linear function, on a convex set, occurs at one of the vertices of the set. Find the vertices and evaluate whatever your object function is.