Instructions: For the given real-world scenario, write the constraints, find the vertices of the feasible region, write the optimization equation, and find the maximum value. Beth is knitting mittens and gloves. Each pair must be processed on three machines. Each pair of mittens requires 2 minutes on Machine A, 2 minutes on Machine B, and 4 minutes on Machine C. Each pair of gloves requires 4 minutes on Machine A, 2 minutes on Machine B, and 1 minute on Machine C. Machine A, B, and C are available 32, 18, and 24 minutes, respectively, everyday. The profit on a pair of mittens is $8.00 and on a pair of gloves is $10.00. Using the information in the problem, write the constraints. Let a represent the number of pairs of mittens made, and y represent the number of pairs of gloves. Total number of time that can be used on Machine A: x+ y Total number of time that can be used on Machine B: Total number of time that can be used on Machine C: x+ x+ 6 4 y How can we show that she cannot make a negative number of mittens?: How can we show that she cannot make a negative number of gloves?: y Vertices of the feasible region: (0, 0)(2, Optimization equation: Profit = x+ )(0, y ,0) ( Beth's maximum profit is $ pairs of gloves each day. per day. She should make pairs of mittens and