5) (16 Points, pproximate time allocated 12 minutes) pet food. eed Company recei

Question

5) (16 Points, pproximate time allocated 12 minutes) pet food. eed Company receives four raw grains from which it blends its dry daily requirements for vitamin C, p well as the vitamin C, protein, and summarized in the following table: The pet f ood advertises that each 12-ounce packet meets the minimum rotein and iron. The cost of each raw grain as iron units per pound of each grain are Vitamin C Protein Iron Grain Units/lb Units/lb Units/lb Costlb Oats Wheat Soy Barley 1.10 2.00 0.75 1.00 16 10 10 14 15 10 Ferdinand is interested in producing the 10-ounce mixture at minimum cos meeting the minimum daily requirements of 8 units of vitamin C, 4 units of protein, and 7 units of iron. (HINT: There are 16 ounces in 1 pound) Assume the decision variables are: O Pounds of Oats W-Pounds of Wheat s Pounds of Soy B Pounds of Barley Define the objective function: Define the constraints: (Hint there are five)

Explanation / Answer

Answer:

As per given data,

n is the Decision variables

O=pounds of oats
W=pounds of wheat
S=pounds of Soy
B=pounds of Barley

Here ,used in the 10-ounce mixture

n Objective functions:

Minimize the total cost for an 10-ounce mixture:

MIN 1.10 O + 2.00W + .75S + 1.00B

n Constraints are :

            Total weight of the mix is 10-ounces (.625 pounds):

                        (1) O + W + S + B = .625

            Total amount of Vitamin C in the mix is at least 8 units:

                        (2) 9O + 16W+ 8S + 10B > 8

            Total amount of protein in the mix is at least 4 units:

                        (3)   10W + 10S + 8B > 4

            Total amount of iron in the mix is at least 7 units:

                        (4) 8O +14W + 15S + 7B > 7

Non-negativity of variables are: O,W,S,B> 0

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