Question $1$:

John Doe has to choose how many sandwiches to make in advance of each day before he knows the actual demand. If left overnight, the sandwiches will be off and be unable to be sold.

His choice is between $40,50,60$ and $70$ sandwiches.

The actual demand can also vary between $40,50,60$ and $70$ with the probabilities as shown in the table $-$ e$.$g$.$ P$($demand $=40)$ is $0\mathrm{.}2.$

The table then shows the profit or loss, for example, if he chooses to make $70$ but demand is only $50,$ then he will make a loss of $$75\mathrm{.}00.$

Daily Demand

Probability

Daily Supply

$40$

$50$

$60$

$70$

$40$

$0\mathrm{.}2$

$$100\mathrm{.}00$

$$0\mathrm{.}00$

$$(100\mathrm{.}00)$

$$(200\mathrm{.}00)$

$50$

$0\mathrm{.}2$

$$100\mathrm{.}00$

$$125\mathrm{.}00$

$$25\mathrm{.}00$

$$(75\mathrm{.}00)$

$60$

$0\mathrm{.}3$

$$100\mathrm{.}00$

$$125\mathrm{.}00$

$$150\mathrm{.}00$

$$(25\mathrm{.}000)$

$70$

$0\mathrm{.}3$

$$100\mathrm{.}00$

$$125\mathrm{.}00$

$$150\mathrm{.}00$

$$175\mathrm{.}00$

Using the minimax, maximax, minimax regret theorem, determine the optimal number of sandwiches John Doe should produce per day.