solve $5-2$ to $5-5$

$5-2.$ A commercial orchard grows, picks, and packs apples and pears. A peck $($quarter bushel$)$ of

apples takes four minutes to pick and five minutes to pack; a peck of pears takes five minutes

to pick and four minutes to pack. Only one picker and one packer are available. How many

pecks each of apples and pears should be picked and packed every hour $(60$ minutes$)$ if the

profit is $$3\mathrm{.}00$ per peck for apples and $$2\mathrm{.}00$ per peck for pears? Solve graphically as a linear

program and confirm analytically.

$5-3.$ Solve the drilling problem $($Table $5-3)$ by using a decision tree.

$5-4.$ You must decide whether to buy new machinery to produce product $x$ or to modify existing

machinery. You believe the probability of a prosperous economy next year is $0\mathrm{.}6$ and of a

recession is $0\mathrm{.}4.$ Prepare a decision tree, and use it to recommend the best course of action.

The applicable payoff table of profits $(+)$ and losses $(-)$ is:

$5-5.$ If you have no idea of the economic probabilities $p_j$ in Question $5-4,$ what would be your

decision based on uncertainty using $($a$)$ maximax, $($b$)$ maximin, $($c$)$ equally likely, and

$($d$)$ minimax regret assumptions?