Salemach Corporation Is a Start-Up Company That Manufactures Simple Machines

question 3

Essay

Salemach Corporation is a start-up company that manufactures simple machines. It is interested in analyzing the profit from a new machine. It estimates that the selling price will be $150 per unit and the setup and advertising costs will total $250,000. The company estimates that the per unit raw material cost is uniformly distributed between $50 and $80 and are equally likely. The demand is normally distributed with a mean of 12,000 units and a standard deviation of 3000 units. The probability distribution for a range of labor cost per unit is given below. $$\begin{array} { c | c } \text { Labor Cost } & \text { Probability } \\\hline \$ 52 & 0.05 \\\$ 53 & 0.25 \\\$ 54 & 0.40 \\\$ 55 & 0.25 \\\$ 56 & 0.05\end{array}$$ ​
a. Obtain estimates for the mean profit, maximum profit, minimum profit, and standard deviation of profit.
b. What is your estimate of the probability of a loss?

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Definitions:

Football Players

Individuals who participate in football, a team sport involving the kicking of a ball to score goals or points.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values, indicating how spread out the data points are from the mean.

Normally Distributed

A distribution where probabilities are mirrored on either side of the mean, illustrating higher frequency of events near the average.

Life Expectancy

The average number of years that an individual or a certain group of individuals is expected to live, based on statistical averages.