Problem $4.$ Johnson Marketing is interested in producing and selling an innovative new food processor. The decision they face is the typical "make or buy" decision often faced by manufacturers. On one hand, Johnson could produce the processor itself, subcontracting different sub$-$assemblies, such as the motor or the housing. Cost estimates in this case are as follows:

Alternative: Make Food Processor

The company also could have the entire machine made by a subcontractor. The subcontractor, however, faces similar uncertainties regarding the costs and has provided Johnson Marketing with the following schedule of costs and chances:

Alternative: Buy Food Processor

a$)$ If Johnson Marketing wants to minimize its expected cost of production in this case, should it make or buy? $(10$ points$)$

b$)$ Construct cumulative risk profiles to support your recommendation. $(10$ points$)$

c$)$ Does one alternative deterministically dominate the other? Why or why not? $(5$ points$)$

d$)$ Does one alternative stochastically dominate the other? Why or why not? $(5$ points$)$