# 3. Dahlby Outfitters wishes to introdu are seeds, raising, flakes, and two k a

Question

# 3. Dahlby Outfitters wishes to introdu are seeds, raising, flakes, and two k amounts of vitamins, minerals, proteins, be designed so that a certain minimum nutritional profile is met. The decision is to ce packaged trail mix as a new product. The ingredients for the trail mix inds of nuts (i.e., pecans and walnuts). Each ingredient contains certain and calories. The marketing department has specified that the product determine the optimal product composition-that is, to minimize the product cost by choosing the amount for each ingredient in the mix. The following data summarizes the parameters of the problem: Units per Pound Nutritional Components Vitamins Minerals Protein Calories Seeds 10 5 Raisins Walnuts Requirements Flakes 10 4 10 160 Pecans 20 10 15 600 20 30 20 4 450 2 300 500 500 Cost/pound $4 $5 $3 $7 $6

Explanation / Answer

Let S, R, F, P and W denote product names. We can solve this as follows.

Total Cost = 4S+5R+3F+7P+6W

Rewriting the above statement as –

Zmin = 4S+5R+3F+7P+6W

subject to constraints –

Vitamin content 10S + 20R + 10F + 30P + 20W greater than or eq 20

Mineral content 5S + 7R + 4F + 9P + 2W greater than or eq 10

Protein content 1S + 4R + 10F + 2P + 1W greater than or eq 15

Calorie content 500S + 450R + 160F + 300P + 500W greater than or eq 600

Rewriting the above constraints as linear equations as given below,

10S + 20R + 10F + 30P + 20W 20

5S + 7R + 4F + 9P + 2W 10

1S + 4R + 10F + 2P + 1W 15

500S + 450R + 160F + 300P + 500W 600

For excel prepare the data set. G9 This would be our minimizing figure

In the given data the cost of each product is already given. So, our aim is to find how much amount of each product shall be produced. This would be the decision variable. We need to find out.

Let’s write the constraints now. We need to find how much vitamin, mineral etc to be added in our product.

Let’s open the Solver now and do the following.

We would take 24.6, 10, 15, 600 for vitamins, minerals, protein and calories. Linear programming suggests us to avoid pecans and walnuts.

0.5 x seeds, 0.3 x Raisins and 1.3 x Flakes are sufficient.

With this, we would be able to provide 24.6 vitamins, 10 minerals, 15 protein and 600 calories.

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