What Is the Optimal Selling Price for a Paint Mixture with 17.0% Pigment?

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Homework Help Overview

The problem involves determining the optimal selling price for a paint mixture containing 17.0% pigment, given the selling prices of other mixtures with different pigment concentrations. The context includes considerations of profit margins and production costs.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for additional information, such as production costs and profit margins of existing mixtures. Some explore mathematical relationships between the pigment concentrations and selling prices, while others question the assumptions made regarding profit on the other mixtures.

Discussion Status

The discussion is ongoing, with participants raising valid points about missing information and exploring different assumptions. There is no explicit consensus, but various approaches to the problem are being considered.

Contextual Notes

Participants note the lack of information regarding production costs and the profit margins on the existing paint mixtures, which are critical for determining the selling price of the new mixture.

jimithing
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A paint mixture containing 25.0% pigment and the balance water sells for $18.00/kg, and a mixture containing 12.0% pigment sells for $10.00/kg. If a paint retailer produces a blend containing 17.0% pigment, for how much ($/kg) should it be sold to yield a 10% profit?

Am I wrong, or are they lacking information (i.e. cost of production, etc.)
this is driving me nuts... :confused:
 
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I would say yes you are missing some information. How much profit is made on the 25% and 12% mixtures comes to mind and as you said production costs... You can make some assumptions like the 25% and 12% mixtures are sold at 10% profit or the like.

Well, good luck.
 
i assumed that the 25% and 12% mixtures were sold at cost, so i used
.25x + .75y = 18
and
.12x + .88y = 10

solved for x and y, then substituted into .17x + .83y = z
found z, multiplied by 1.1

hopefully that's what they're looking for
 
"Interactive math program"?
 

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