The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $ $45$ ?per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

Procurement Cost $($ $ $)$

Probability

Labor Cost $($ $ $)$

Probability

Transportation Cost $($ $ $)$

Probability

$10$

$0\mathrm{.}25$

$20$

$0\mathrm{.}10$

$3$

$0\mathrm{.}75$

$11$

$0\mathrm{.}45$

$22$

$0\mathrm{.}25$

$5$

$0\mathrm{.}25$

$12$

$0\mathrm{.}30$

$24$

$0\mathrm{.}35$

$25$

$0\mathrm{.}30$

$($ a $)(2$ ?marks $)$ ?Calculate the expected value of the procurement, labor, and transportation cost, respectively.

$($ b $)(5$ ?marks $)$ ?Use the following random numbers $($ procurement $,$ ?labor, and transportation cost, respectively $)$ ?to calculate a potential value for the unit profit: $0\mathrm{.}005,0\mathrm{.}26,$ ?and $0\mathrm{.}87.$