Please include a excel sheet on how to do this.

The Candy Town Company, a competitor of the SweetTooth Candy Company, knows it will need $40,000$ lbs of sugar six months from now to implement its production plans. James Taffy, Candy Town's purchasing manager, has essentially two options for acquiring the needed sugar. One option is to buy the sugar at the going market price when they need it$,$ six months from now. Mr$.$ Taffy has assessed the probability distribution for the possible prices of sugar six months from now $($in dollars per pound$)$ as shown below:

Price in $6-$month Probability

$$0\mathrm{.}0780\mathrm{.}10$

$0\mathrm{.}0860\mathrm{.}20$

$0\mathrm{.}0940\mathrm{.}20$

$0\mathrm{.}1020\mathrm{.}20$

$0\mathrm{.}1100\mathrm{.}20$

$0\mathrm{.}1180\mathrm{.}10$

The second purchasing option is to buy a futures contract now. The contract guarantees delivery of the sugar in six months but the cost of purchasing it will be based on today's market price. Assume that possible sugar futures contracts available for purchase are for $10,000$ lbs$,20,000$ lbs or $40,000$ lbs only. No futures contracts can be purchased or sold in the intervening months. The Candy Town Company will buy the total of $40,000$ lbs of sugar in one way or another. The price of sugar now is $$0\mathrm{.}0851$ per pound. The transaction costs for $10,000$ lbs$,20,000$ lbs and $40,000$ lbs futures contracts are $$150,$ $$200,$ and $$350,$ respectively.

Options:

$1.3683$

$2.3754$

$3.3862$

$4.3920$

$5.3941$

$6.$ Buy no futures contract

$7.$ Buy the $10,000$ lbs futures contract

$8.$ Buy the $20,000$ lbs futures contract

$9.$ Buy the $40,000$ lbs futures contract