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Question

# A food company manufactures five types of 8 oz Trail mix packages using different mixtures of peanuts, almonds, walnuts, raisins, and M&Ms. The mixtures have the following compositions: $$ \begin{matrix} \text{ } & \text{Peanuts (oz)} & \text{Almonds (oz)} & \text{Walnuts (oz)} & \text{Raisins (oz)} & \text{M&Ms(oz)}\\ \text{Mix 1} & \text{3} & \text{1} & \text{1} & \text{2} & \text{1}\\ \text{Mix 2} & \text{1} & \text{2} & \text{1} & \text{3} & \text{1}\\ \text{Mix 3} & \text{1} & \text{1} & \text{0} & \text{3} & \text{3}\\ \text{Mix 4} & \text{2} & \text{0} & \text{3} & \text{1} & \text{2}\\ \text{Mix 5} & \text{1} & \text{2} & \text{3} & \text{0} & \text{2}\\ \end{matrix} $$ How many packages of each mix can be manufactured if 128 lb of peanuts, 118 lb of almonds, 112 lb of walnuts, 112 lb of raisins, and 104 lb of M&Ms are available? Write a system of linear equations and solve.

Solution

VerifiedStep 1

1 of 4X= $[3\,\,\,\,1\,\,\,\,1\,\,\,\,2\,\,\,\,1; 1\,\,\,\,2\,\,\,\,1\,\,\,\,0\,\,\,\,2;\\ 1\,\,\,\,1\,\,\,\,0\,\,\,\,3\,\,\,\,3 ; 2\,\,\,\,3\,\,\,\,3\,\,\,\,1\,\,\,\,0; 1\,\,\,\,1\,\,\,\,3\,\,\,\,2\,\,\,\,2]$;

Assume we can make a packages of Mix 1, b packages of Mix 2, c packages of Mix 3, d packages of Mix 4 and e packages of Mix 5.

we have the data of mixtures in Ib and we make packages with ounces so we have to multiply the data of the materials (128, 118, 112, 112, 104) by 16.

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