The assignment must be completed in groups of two unless otherwise is permitted by the instructor. You must hand-write your answers and submit a scanned version (scanning/taking pictures with phone is ok) to Canvas. You must combine those several pages of scans/pictures of your handwritten answers into one Word or PDF file only (do not submit the scans/pictures separately). The assignment should be submitted to Canvas by one of the group members only (write the names of all team members on the assignment). Handwriting on iPad, Surface, etc. is accepted, but typing is not allowed. You are responsible for making sure the handwriting is neat to read and the scanned copy/picture is of high-quality. No late assignments will be accepted for any reasons, and zero grade will be assigned. Do not forget to include units in your model, etc., wherever required. You will lose marks if you do not include units properly. Jim's Pumpkin Muffins Bakery Pumpkin Muffins sells two types of muffins: Kale, and Carrot. The profits for Kale and Carrot muffins are $2/muffin, $3/muffin respectively. Jim, the owner of Pumpkin Muffins, must decide how many of each type of muffins to make. Jim knows that he can sell at most 45 muffins per day and must not make more than he may sell. Jim can spend at most 2 labor hours per day and has 5 hours of baking time. The labor and baking requirements for making the muffins are summarized in the following table. Labor Time (minutes/muffin) Baking Time (minutes/muffin) Carrot Kale 3 4 10 7 Each morning, Jim sells at least 10 Kale, and 5 Carrot muffins to the nearby supermarket, so he must meet these production minimums. Jim would like to maximize profit while meeting all the constraints. a) Formulate this linear programming problem and provide the mathematical representation of the model. Do not build/solve the model in Excel. Clearly explain the decision variables, state the units of each constraint and clearly label your constraints. Make sure your model includes all the required components of the LP mathematical formulation. b) Solve your LP model graphically. Clearly identify the feasible region and draw one or more isoprofit lines. Clearly show the direction of improvement for the isoprofit lines. c) What is the optimal solution? What is the optimal objective value? Explain in words what each of them mean. d) How many feasible solutions does the model have? e) How many feasible corner points does the model have? f) Which constraints are binding? Which constraints are non-binding? Explain why; do not just mention the constraints. g) Bonus question (only this part (g) is optional and is worth 10/100 only if your answer is fully correct; no partial credits): which constraints are redundant? h) Suppose Jim's car breaks down on the way to the bakery, and as a result of that, he now has only 1.5 hours of baking time instead of 2. His labor time availability is unchanged. How would this change affect the feasible region? Feel free to draw a new graph or explain/show it in your original graph, making sure everything is neat and readable. How many feasible points do we have now? What is the optimal solution?