307w.WLCA.C10 computations are linear?

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Discussion Overview

The discussion revolves around computations related to a mixture problem involving different ingredients (raisins, peanuts, and chocolate) and their associated costs. Participants are exploring the formulation of these computations, particularly in the context of linear algebra notation and matrix representation.

Discussion Character

  • Technical explanation, Mathematical reasoning, Homework-related

Main Points Raised

  • One participant presents a matrix from a source (eMH) but expresses uncertainty about its correctness.
  • Another participant outlines the mathematical formulation for the cost of different mixes based on the quantities of ingredients, introducing variables for each ingredient.
  • A participant suggests using linear algebra notation ($x_1, x_2, x_3$) for clarity in the matrix representation.
  • A correction is made regarding a typo in the cost calculation, clarifying the correct coefficients for each ingredient in the cost formula.

Areas of Agreement / Disagreement

The discussion contains some corrections and clarifications, but there is no consensus on the overall approach or correctness of the initial matrix presented.

Contextual Notes

There are unresolved issues regarding the accuracy of the initial matrix and the implications of the cost calculations, which depend on the correct interpretation of the variables and coefficients.

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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