3. Suppose that the mill in Problem 2 has decided to launch with three product types: blankets, rugs, and sweaters. You have been given the following updated table of labor hours needed to produce one of each of the products (by product-ion phase) made at the mill: The following table gives the weekly labor hours needed required to produce one of each of the products (by product-ion phase) made at the mill: Blankets Rugs Sweaters Spinning s 4 ' 4 Weaving 4 5 6 Dyeing 9 3 I 2 Cutting 2 2 3 Recall that the mill has 1080 labor hours available for Spinning, 850 labor hours available for weav ing, 1170 labor hours available for dyeing, and 360 labor hours available for cutting each week. You are also told that the mill anticipates making an average of $55 for each blanket it produces, $50 for each rug it produces, and $45 for each sweater it produces. (a) [5 points] Dene variables for this scenario, write down the objective function, and identify the constraint-s in this problem. In other words, write down the full linear programming problem that models this scenario. (b) [10 pointS] Solve the linear programming problem, and give a recommendation for the optimal number of products that should be produced each week. When making your recommendation, refer to your work for Problem 2