Question $1$: Expected Monetary Value $(13$ points$)$

The yearly demand for a seasonal, profitable item follows the distribution below:

Product Demand $($units$)$ Probability

$15,0000\mathrm{.}25$

$25,0000\mathrm{.}40$

$35,0000\mathrm{.}20$

$45,0000\mathrm{.}15$

A seasonal product manufacturer is considering launching a project to produce this item and could produce it by one of three methods:

Method A

$$ Use existing tools at a cost of $$75$ per unit

$$ Annual cost of new special equipment is $$0.$

Method B

$$ Buy cheap, special equipment for $$15,000,$ i$.$e$.,$ annual cost

$$ The value of the equipment at the end of the year $($salvage value$)$ is zero. The cost would be reduced to $$45$ per unit.

Method C

$$ Buy high$-$quality, special equipment for $$100,000$ that can be depreciated over four years, i$.$e$.,$ annual cost is $$25,000$ each year. The cost with this equipment would be only $$35$ per unit.

Required:

$$ Use the expected monetary value $($EMV$)$ criterion to determine whether the manufacturer should approve this project

$$ If you determine that the project should be approved, which method of production should the manufacturer use to maximize profit?