Question $(1)$: Choose the most correct answer for the following statements And explan how to get the correct answer by steps

Problem $1$: Mohamed is about to install a new machine for making parts for domestic appliances. He has three alternative machines to choose from $($with no option for doing nothing$).$

Machine $1$: it automatically produces parts of acceptable, but not outstanding, quality. The output from the machine varies $($depending on the materials used and a variety of settings$)$ and might be $1,000$ a week $($with probability $0\mathrm{.}1),2,000$ a week $($with probability $0\mathrm{.}7)$ or $3,000$ a week. The notional profit for this machine is $$8$ a unit.

Machine $2$: it makes higher quality parts. The output from this might be $700$ a week $($with probability $0\mathrm{.}4)$ or $1,000$ a week, with a notional profit of $$20$ a unit.

Machine $3$: it can be set to produce either $1,300$ highquality parts a week at a profit of $$12$ a unit, or $1,600$ medium quality parts a week with a profit of $$10$ a unit.

If the machine produces $2,000$ a week, Mohamed can export all production as a single bulk order. Then there is a $60\%$ chance of selling this order for $50\%$ more profit, and a $40\%$ chance of selling for $50\%$ less profit.

$(1)$

EMV $($node $1)=..........$

A$)17,600,$

B$)20,000,$

C$)17,650,$

D$)16,700,$

E$)17,610,$