# Paul has to buy two types of Yogurts- Brand A and Brand B for children. He knows the following regarding the Vitamins the yogurts have: 3) Vitamin A Vitamin B Vitamin C Brand A 15 15 10 20 Brand B 10 The price of Brand A is \$1.25 and Price of Brand 8 is \$1.50. Paul wants to make sure the children get at least 200 unit of Vitamin A, 150 unit of Vitamin B, and 150 unit of Vitamin C. Moreover, the number of Brand B has to be at least twice the number of Brand A yogurts Using linear programming find the minimum cost of buying the yogurts to provide the required units of vitamins. How many of each type of yogurt Paul should buy to keep the cost at the minimum. (a) (b) (For 5 Extra creditpoints) After going to the store if Paul finds out that only 5 of Brand A yogurt is available then how many of each type of yogurt Paul should buy? What will be his cost of purchasing yogurts in this new situation? https://d2vlcm61l7u1fs.cloudfront.net/media%2F1ce%2F1cef0984-0fdf-46ee-ab0d-a106aaa5f08e%2Fimage

(a) Solution using Linear programming approach is as follows

https://d2vlcm61l7u1fs.cloudfront.net/media%2F1a7%2F1a7d5cc3-5dea-4637-ae71-d4df891c9b08%2FphpMfYkQn.png
Formula:

D2 =SUMPRODUCT(B2:C2,\$B\$9:\$C\$9) copy to D2:D5, D7

Minimum cost of the buying the yoghurts = \$ 25.5

Number of brand A = 6

Number of brand B = 12

(b) The new model and solution is as follows
https://d2vlcm61l7u1fs.cloudfront.net/media%2F354%2F3542877e-15d2-4e8e-b8c0-1d1ce73f1636%2FphpKoAJxc.png

Number of brand A = 5

Number of brand B = 15

Minimum total cost = \$ 28.75

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