MHB 307w.WLCA.C10 computations are linear?

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The discussion focuses on the linearity of computations related to the costs of ingredients in different mixes. It clarifies the equations for calculating the total cost of "Bulk," "Standard," and "Fancy" mixes based on the quantities of raisins, peanuts, and chocolate. A correction is made regarding a typo in the cost calculation, emphasizing the correct coefficients for each ingredient. The conversation also touches on the preferred notation for variables in linear algebra. Understanding these computations is essential for accurate cost analysis in product formulation.
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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).
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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