SOLUTION: Sergio runs a bakery that sells two kinds of desserts. Sergio knows the bakery must make at least 29 and at most 48 batches of the White Chocolate Blizzards. The bakery must also m

Question 1133589: Sergio runs a bakery that sells two kinds of desserts. Sergio knows the bakery must make at least 29 and at most 48 batches of the White Chocolate Blizzards. The bakery must also make between 6 and 36 batches of the Nutty Squirrels. The batches of White Chocolate Blizzards take 9 ounces of flour, while batches of Nutty Squirrels require 16 ounces of flour. The bakery only has 864 ounces of flour available. If batches of White Chocolate Blizzards generate $1.75 in income, and batches of Nutty Squirrels generate $1.73, how many batches of the desserts should Sergio have the bakery make to get the most income?
How do I set up this up? I believe it is a linear program question. I have tried 29x+48y=9, 6x+36y=16 and the z function of z=1.75x+1.73y
I believe it's wrong since I am getting decimals as an answer...
Please help thank you...

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The problem is poorly formulated, because the given information yields a feasibility region with corners that have coordinates that are not whole numbers, making it exceedingly difficult to find the answer to the problem.

I will go ahead and help you see how to set up the problem for solving; I hope that much will be of some help to you.

It looks as if you don't have a clear understanding of what your "x" and "y" represent, and you are just writing equations using the numbers in the problem without understanding what those numbers mean. You use some of the numbers in the problem in ways that make no sense; and you don't use some of the critical numbers.

The unknowns x and y are the numbers of batches of the two kinds of desserts. Based on that, your objective function x = 1.73x+1.75y makes sense -- the profit is $1.73 for each of the x batches of Nutty Squirrels and $1.75 for each batch of the White Chocolate Blizzards.

The 29 and 48 in the problem are the least and greatest numbers of batches of White Chocolate Blizzards that the company can make; the 6 and 36 are the least and greatest numbers of batches of Nutty Squirrels the company can make. Since x and y are the numbers of batches of each kind of dessert, that information tells you

6 <= x <= 36
29 <= y <= 48

The only constraint in the problem, other than the minimum and maximum numbers of each kind of dessert, is the number of ounces of flour available. There are 864 ounces of flour available; each batch of White Chocolate Blizzards takes 9 ounces of flour, and each batch of Nutty Squirrels requires 16 ounces of flour. The constraint is then

9x+16y <= 864.

So the constraints on the numbers the two kinds of desserts, which determine the feasibility region, are

(1) 6 <= x <= 36
(2) 29 <= y <= 48
(3) 9x+16y <= 864

The corners of the feasibility region based on those constraints are

(6,29), (6,48), (32/3,48), and (400/9,29).

As I said at the beginning of my response, those non-integer coordinates make the problem solvable only by extensive guessing, from which you gain no useful mathematical knowledge.
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