Problem 5. (20 pts) PDQ manufacturing company produces two products, widgets and gadgets. Each widget and...

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Problem 5. (20 pts) PDQ manufacturing company produces two products, widgets and gadgets. Each widget and gadget requires several basic ma- chining operations to produce. PDQ has five different machining centers, and some of the required machining operations can be performed at more than one of the centers. Consequently, there are several alternative ways of producing each widget and each gadget. Table below summarizes the unit production times required for the various operations. Unit production times (hours) Center 2 Center 3 Center 4 Center 5 Product Method Center 1 1 0.25 0.13 0.20 Widget 2 - 0.34 0.15 - 0.28 3 0.25 0.42 1 0.18 0.32 2 0.26 0.22 0.14 Gadget 3 0.20 0.30 4 0.12 0.18 0.20 The unit cost of widgets produced using Methods 1, 2, and 3 are $1.35, $1.28, and $1.47, respectively. Similarly, the unit cost for gadgets produced using Methods 1, 2, 3, and 4 are $1.14, $1.19, $1.26, and $1.16, respectively. The weekly demand for widgets and gadgets are 320 and 250, respectively, and each machining center is available for 80 hours per week. Formulate a linear programming problem to find the least-cost production schedule. Furthermore, code and solve the problem in CVXPY following the instruction in this homework. Problem 5. (20 pts) PDQ manufacturing company produces two products, widgets and gadgets. Each widget and gadget requires several basic ma- chining operations to produce. PDQ has five different machining centers, and some of the required machining operations can be performed at more than one of the centers. Consequently, there are several alternative ways of producing each widget and each gadget. Table below summarizes the unit production times required for the various operations. Unit production times (hours) Center 2 Center 3 Center 4 Center 5 Product Method Center 1 1 0.25 0.13 0.20 Widget 2 - 0.34 0.15 - 0.28 3 0.25 0.42 1 0.18 0.32 2 0.26 0.22 0.14 Gadget 3 0.20 0.30 4 0.12 0.18 0.20 The unit cost of widgets produced using Methods 1, 2, and 3 are $1.35, $1.28, and $1.47, respectively. Similarly, the unit cost for gadgets produced using Methods 1, 2, 3, and 4 are $1.14, $1.19, $1.26, and $1.16, respectively. The weekly demand for widgets and gadgets are 320 and 250, respectively, and each machining center is available for 80 hours per week. Formulate a linear programming problem to find the least-cost production schedule. Furthermore, code and solve the problem in CVXPY following the instruction in this homework.