Formulate the problem, and solve it by hand using the simplex method:

The Ottawa Coat company manufactures winter coats and spring jackets. The winter coat requires 4 m of material on standard-size rolls while the spring jacket requires just 1 m. The company wants to minimize the consumption of material. Each winter coat has one zipper while each spring jacket has two. The seamstresses can sew in zippers at a top rate of 5 per hour. Winter coats bring a net profit of $4 and spring jackets a net profit of $3. The company requires that the profit rate be at least $6 per hour. Finally, for maximum efficiency in using the material rolls, three times the hourly production of winter coats plus the hourly production of spring jackets, must equal exactly 3. At what hourly rates should the company produce winter coats and spring jackets to minimize the consumption of material? What is the minimum total material consumption rate?