307w.WLCA.C10 computations are linear?

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SUMMARY

The discussion centers on the linear algebra computations required for calculating the costs of different mixes of ingredients: "Bulk," "Standard," and "Fancy." Each mix's cost is derived from the quantities of raisins (x), peanuts (y), and chocolate (z) used, with specific coefficients for each ingredient. The correct cost formula for the "Bulk" mix is established as 7(2.55x) + 6(4.65y) + 2(4.80z), correcting a previous typo that incorrectly included y twice. The use of LA notation for variables is also emphasized for clarity in matrix representation.

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This discussion is beneficial for students and professionals in fields such as mathematics, food science, and supply chain management, particularly those involved in cost analysis and optimization of ingredient mixtures.

karush
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the matrix at the bottom is from eMH but thot this was the way to do it... maybe not!
 
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Do you understand what this table tells you and what you are asked to do?

Let x be the number of kg of raisins used, y the number of kg of peanuts, z the number of kg of chocolate. Then one batch of "Bulk" mix requires 7x+ 6y+ 2z, one batch of "standard' mix requires 6x+ 4y+ 5z, and one batch of "Fancy" mix requires 2x+5y+ 8z.

The bottom row shows the cost of each kg of raisins, peanuts, and chocolate. x kg of peanuts costs 255x, y kg of peanuts cost 4.65y, and z kg of chocolate cost 4.80z so one batch of "Bulk" mix cost 7(4.65y)+ 6(4.65y)+ 2(4.80z)
 
ok I think in LA notation $ x_1, x_2, x_3$ is preferred for the matrix

why do you have y twice in 7(4.65y)+ 6(4.65y)+ 2(4.80z)
 
That was a typo, of course.

It should be 7(2.55x)+ 6(4.65y)+ 2(4.80z).
 

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