An international toy manufacturing company manufactures three types of stuffed animals – dog, lion and giraffe, each made from different combination of red, yellow and blue cloth and cotton. The data (cloth requirement in yards) is as below:

Toy Dog Lion Giraffe Red 1/2 1/2 1.5 Yellow 2 1.5 1.5 Blue 1 1.5 1.5 Cotton (in kg.) 2 3 4 The dog sells at $47.5, lion at $60, and giraffe at

$75. The company has 1500 yards of red, 2000 yards of blue and 200 yards of yellow cloth, while 50,000 kg of cotton is available. Develop and solve a linear optimization model to determine the optimal mix to maximize turnover, and write a short explanation of the sensitivity information.