Please help. Assignment question Linear programming model algebraically

[Muimui0308]

The Knockhill Corporation produces two grades of livestock feed. The grades-nutritious and regular- are produced by refining a blend of two types of raw powder feed- types A and B. Each of them differs not only in cost per barrel, but also in composition. The following table indicated the percentage of crucial ingredients of each of the powder feeds and cost per barrel for each:

Types/ Honey% / Corn Starch% / Cost per barrel
A 40%/ 55%/ $35

B 55%/ 30%/ $40

Weekly demand for the nutritious grade of feed is at least 2,600 barrels and demand for the regular grade is at least 3,400 barrels. At Least 45% of each barrel of the nutritious grade must be honey. At most 50% of each barrel of regular grade should contain corn starch. the product manager of Knockhill Corporation needs to decide how many barrels of each type of raw powder feed to buy each week for blending to satisfy demand at the minimum cost.

Assume that all barrels aforementioned have the same volume. Formulate the linear programming model algebraically for the above problem. (no need to solve the model)

 

[HallsofIvy]

Okay, what kind of "help" do you want? Someone to do the problem for you? That wouldn't help you learn anything. If you want hints and suggestions on how to do this problem yourself, we need to see what you have tried and where you had difficulty.

 

[mmm4444bot]

Please check our FORUM GUIDELINES for information on how to post requests for help.

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Cheers :cool:

 

[Muimui0308]

Okay, what kind of "help" do you want? Someone to do the problem for you? That wouldn't help you learn anything. If you want hints and suggestions on how to do this problem yourself, we need to see what you have tried and where you had difficulty.

Am i think wrong side X=>3,400, Y=>2,600?

Let X be the types A
Let Y be the types B

Min cost= $35X + $40Y

subject to

0.4X+0.55Y=>0.45
0.55X+0.3<=0.5
X=>3,400
Y=>2,600

Contraint X,Y=>0

Thank you.

 

[HallsofIvy]

I am confused by two statements: First that "type B" must be 55% Honey and second that "At Least 45% of each barrel of the nutritious grade must be honey". Which is correct, exactly 55% or at least 45%?

 

[mmm4444bot]

I am confused by two statements: First that "type B" must be 55% Honey and second that "At Least 45% of each barrel of the nutritious grade must be honey". Which is correct, exactly 55% or at least 45%?

Raw material B contains 55% honey. It comes that way from Knockhill's supplier.

It is one of Knockhill's subsequent mixtures (specifically, the one they call Nutritious) that must contain at least 45% honey.

 

[mmm4444bot]

Am i think wrong side X=>3,400, Y=>2,600?

Let X be the types A
Let Y be the types B

You defined symbol X to be "the types A"

That is not very clear. How about the following?

Let X = the number of barrels of raw material A that must be purchased each week

Let Y = the number of barrels of raw material B that must be purchased each week


X >= 3400 is not correct because this exercise does not state that the production manager must purchase 3,400 barrels or more of raw material A.

Y >= 2600 is wrong for similar reasons.

Please read the exercise again.

Min cost= $35X + $40Y

Please do not write dollar signs in your equations.

The expression 35X + 40Y represents the minimum cost only for a specific value of X and a specific value of Y. Those two specific values are what you are trying to determine.

Therefore, do not write "Min cost =" because the expression 35X + 40Y is not always a minimum.

Weekly raw-material cost = 35X + 40Y

0.4X+0.55Y=>0.45

The expression 0.4X + 0.55Y represents the total amount of honey contained within all of the raw material purchased that week (both A and B).

In other words, if you mixed together all of the Nutritious and Regular feed produced that week, the entire pile would contain 0.4X + 0.55Y barrels of honey.

Your inequality above states that all of the honey purchased (that is, coming from both raw materials A and B) must be more than 45% of one barrel. That's not what the exercise says.

Contraint X,Y=>0

This is not correct. The production manager does not have the option of purchasing zero barrels of either raw material types. The exercise makes this clear. Knockhill uses BOTH types.

 

[mmm4444bot]

Hi Jeff: I'm reading the exercise a bit differently, on that point.

The grades-nutritious and regular- are produced by refining a blend of two types of raw powder feed- types A and B.

This statement tells me that each grade is a blend of raw materials A and B. :cool:

---

PS: I tried to quote your quote above, but the quote-quotes feature seems to be broken (still).

 

[Muimui0308]

Weekly raw-material cost= Nutritious grade + Regular grade
Weekly raw-material cost = (35X + 40Y) Nutritious grade + (35X + 40Y) Regular grade

am i right

 

[ajim]

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