The Minnow Bucket Bait Shop in Land O\' Lakes, Wi Rases trout and have 4500 of t

Question

The Minnow Bucket Bait Shop in Land O' Lakes, Wi Rases trout and have 4500 of them. They want to buy a mix of feed for their trout that both provides the nutrients needed and comes at a low cost. In order to do this, they are going to buy a mix of two brands. Each pound if Brand 1 contains 2 ounces of ingredient A, 4 ounces of ingredient B and 0.5 ounces of ingredient C. Each pound of Brand 2 contains 10 ounces of ingredient A, 3 ounces of ingredient B and no ounces of ingredient C. Brand 1 costs $2.20 a pound and Brand 2 costs $3.20 per pound. Each trout needs 85 ounces of ingredient A, 48 ounces of ingredient B and 2.5 ounces of ingredient C per mont.

How many total pounds of each brand should they buy per month to keep their cost as low as possible and still meet their dietary requiements of the trout? What will the cost per month be?

Include your spreadsheet with any formuals noted. Also include a list of the constraints you used.

Explanation / Answer

$3.15

Requirement of a Trout per Month is,

2.5 Ounces of C

So, the remaining balance of Ounces we will get from Brand 2

Each pound of Brand 1 contains, Ingredient A 3 Ounces Ingredient B 4 Ounces Ingredient C 0.5 Ounces Cost of 1 Pound of Brand 1 $2.15 Each pound of Brand 2 contains, Ingredient A 10 Ounces Ingredient B 3 Ounces Ingredient C - Cost of 1 Pound of Brand 2

$3.15

Each pound of Brand 1 contains, Ingredient A 3 Ounces Ingredient B 4 Ounces Ingredient C 0.5 Ounces Cost of 1 Pound of Brand 1 $2.15 Each pound of Brand 2 contains, Ingredient A 10 Ounces Ingredient B 3 Ounces Ingredient C - Cost of 1 Pound of Brand 2 $3.15

Requirement of a Trout per Month is,

85 Ounces of A 48 Ounces of B

2.5 Ounces of C

So, the requirement per month for 4500 trouts is, 85 * 4500 = 3,82,500 Ounces of A 127500 38250 48 * 4500 = 2,16,000 Ounces of B 54000 72000 2.5 * 4500 = 11,250 Ounces of C 22500 Being there is no Ingredient C available in Brand 2, we should compulsary buy atleast 22,500 Pounds of Brand 1 In 22,500 Pounds of Brand 1, we will get 67,500 (22,500*3) Ounce of A, 90,000 Ounces of B.

So, the remaining balance of Ounces we will get from Brand 2

Remaining required Ounces are as follows, A = 3,82,500 - 67,500 = 3,15,000 B = 2,16,000 - 90,000 = 1,26,000 31,500 (3,15,000 / 10 Ounces) Pounds of Brand 2 is to be purchased So, total Cost = (22,500 * $2.15) + (31,500 * $3.15)                            = $48,375 + $99,225                            = $1,47,600

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