Question 2 The FunnyBear Company manufactures and markets stuffed animal dolls for both kids and adults. Currently, the company produces two models: full-size and compact. Production is limited by the amount of labour available in the general assembly and electronic sewing departments, as well as by the demand for each model. Each full-size stuffed doll requires 2 hours of general assembly and 1 hour of electronic sewing, whereas each compact doll requires 1 hour of general assembly and 1 hour of electronic sewing. In the current production period. there are 400 hours of general assembly labour available and 350 hours of electronic sewing labour available. The company estimates that it can sell at most 150 full-size dolls and 200 compact dolls in the current production period. The earnings contribution per doll is $25 for a full-size doll and $20 for a compact doll. The company would like to nd an earnings-maximizing production plan for the current production period. (a) Formulate the above problem as a linear optimization model. State the objective function as well as the necessary constraints. (8 marks) (b) Without actually solving the linear optimization model, describe an alternative approach to nd the optimal solution. What is the value of the objective function at the optimal solution? (10 marks) (c) List two (2) possible conditions required for the proposed solution in (b) to work. (10 marks) Question 3 Based on the context in Question 2, the FunnyBear Company is planning for future productions. While most aspects of the problem are the same as before, two aspects are not certain: o The unit contribution to earnings of selling full-sized dolls is uncertain due to uctuations in the market. Suppose the estimated unit contribution to earnings of full-size dolls will be in the range between $22 and $35. For the sake of simplicity, let us suppose that this unit earnings contribution will be either $22 (with a probability of 0.5) or $35 (with a probability of 0.5). o The capacity for the general assembly labour hours is uncertain. There are more available workers in the free market. Let us suppose the general assembly labour hours for the next quarter will be either 400 hours (with probability 0.4) or 500 hours (with probability 0.6). The company needs to decide whether it should continue its operation or terminate the current business plan. (a) (1)) Decide the objective of this problem considering the given uncertainties. Are you conservative or optimistic? Justify your answers. (10 marks) If you are a risk-neutral decision maker, evaluate the given details and then formulate this optimization problem under uncertainty. (1 7 marks)