A commercial customer has ordered 104 gallons of paint that contains an equal am

Question

A commercial customer has ordered 104 gallons of paint that contains an equal amount of red paint, yellow paint, green paint, and blue paint, and hence could be prepared by mixing 26 gallons of each color. However, the store wishes to prepare this order by mixing four types of paint that are already available in large quantity: Paint A is a mixture of 50.5% red, 9.5% yellow, 20% green, and 20% blue paint; Paint B is a mixture of 10% red, 2.5% yellow, 70% green, and 17.5% blue paint; Paint C is a mixture of 5% red, 20% yellow, 15% green, and 60% blue; and Paint D is a mixture of 15.5% red, 65.5% yellow, 4% green, and 15% blue. How many gallons of paints A, B, C, D are needed to prepare the customer's order? Write out a system of equations that represents the information given, then solve that system using Maple, Matlab, Wolfram alpha, or any other favorite mathematical software.

Explanation / Answer

clc;

close all;

clear all;

%% Program starts here

mix_mat=[0.505 0.095 0.2 0.2

0.1 0.025 0.7 0.175

0.05 0.02 0.15 0.6

0.155 0.655 0.04 0.15

];

mat=mix_mat';

disp('The proportion of A B C and D is :')

PAINT=inv(mat)*[26;26;26;26]

OUTPUT:

The proportion of A B C and D is :

PAINT =

35.3468

21.5084

16.9705

33.2289

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