Kalamazoo Kennels provides overnight lodging for a variety of pets. An attractiv

Question

Kalamazoo Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows: Cat Food Cost/oz protien (%) fat (%) Pet's Choice 0.35 40 15 Feline Chow 0.32 20 30 Kalamazoo Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Note: Please write your answers with two significant places after the decimal and do not include the dollar “$” sign. For instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45

Explanation / Answer

let x ounce of feline chow

y ounce of Kalamazoo Kennels

minimize 0.35x + 0.32 y

subject to 0.4 x+0.2 y >=5

0.15x + 0.3 y >=3

Solution :

Vertex Lines Through Vertex Value of Objective
(10,5) 0.4x+0.2y = 5; 0.15x+0.3y = 3 5.1 Minimum
(0,25) 0.4x+0.2y = 5; x = 0 8
(20,0) 0.15x+0.3y = 3; y = 0 7

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