Question

Quick easy questions! Just a few!

The SweetTooth Candy Company knows it will need 10 tons (20,000 lbs) of sugar six months from now to implement its production plans. Jean Dobson, SweetTooth's purchasing manager, has essentially two options for acquiring the needed sugar. One option is to by buy the sugar at the going market price when she needs it, six months from now. Ms. Dobson 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
$0.078    0.05
   0.083    0.25
   0.087    0.35
   0.091    0.20
   0.096    0.15     

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'smarket price. Assume that possible sugar futures contracts available for purchase are for five tons or ten tons only. No futures contracts can be purchased or sold in the intervening months. Thus, SweetTooth's possible decision alternative are to (1) purchase a futures contract for ten tons of sugar now, (2) purchase a futures contract for five tons of sugar now and purchase five tons of sugar later in six months, or (3) purchase all ten tons of needed sugar later in six months. The price of sugar now is $0.0851 per pound. The transaction costs for five-ton and ten-ton futures contracts are $65 and $110, respectively.

Question 8 (1 point)

The best decision alternative by the Maxmin method is

Question 8 options:

	Buy the futures contract for 10 tons.
	Buy the futures contract for 5 tons.
	Buy the futures contract for 2.5 tons.
	Buy the futures contract for 0 ton.

Question 9 (1 point)

The best decision alternative by the Maxmax method is

Question 9 options:

	Buy the futures contract for 10 tons.
	Buy the futures contract for 5 tons.
	Buy the futures contract for 2.5 tons.
	Buy the futures contract for 0 ton.

Question 10 (1 point)

The expected cost of buying the futures contract for 10 tons is

Question 10 options:

	1702
	1812
	1793
	1754

Question 11 (1 point)

The expected cost of buying the futures contract for 5 tons now is

Question 11 options:

	1812
	1702
	1754
	1793

Question 12 (1 point)

The expected cost of not buying the futures contract is

Question 12 options:

	1754
	1812
	1793
	1702

Question 13 (1 point)

The best decision alternative by the expected value method is

Question 13 options:

	Buy the futures contract for 10 tons.
	Buy the futures contract for 5 tons.
	Buy the futures contract for 2.5 tons.
	Buy the futures contract for 0 ton.

Answer 1

SweetTooth's possible decision alternative are to

1. purchase a futures contract for ten tons of sugar now, same as Buy the futures contract for 10 tons.
2. purchase a futures contract for five tons of sugar now and purchase five tons of sugar later in six months, same as Buy the futures contract for 5 tons.
3. purchase all ten tons of needed sugar later in six months, same as Buy the futures contract for 0 ton

The decison tree with the cost of purchase are given below

The cost of purchasing 10 tons of sugar for 3 decision alternatives are below

1. Buy the futures contract for 10 tons.

That means but 10 tons (20,000lbs) of sugar at the current price of $0.0851 per pound + the cost of contract

Cost = $0.0851*20000+110 =$1,812

2. Buy the futures contract for 5 tons (10,000 lbs) and buy the rest 5 tons (10,000 lbs) 6 months from now as per the prevailing prices then

That means but 5 tons/10,000lbs of sugar at the current price of $0.0851 per pound + the cost of contract +10,000 pounds as per the price schedule

There are 5 possible prices

• Cost = 0.0851*10000+65+0.078*10000 = $1,696

• cost= 0.0851*5*20000+65+0.083*5*20000 = $1,746

• cost= 0.0851*5*20000+65+0.087*5*20000 = $1,786

• cost= 0.0851*5*20000+65+0.091*5*20000 = $1,826

• cost= 0.0851*5*20000+65+0.096*5*20000 = $1,876  

Since the optimum solution is to minimize the cost, ??for Maxmin approach we take minmax approach.

The maximum profit/minimum cost = $1,696

Minimum profit/maximum cost = $1,876  

Assuming V(price) = payoff/cost of 10 tons of sugar at the price and P(price) = probability of that price

The expected value is calculated as

3)

2. Buy the futures contract for 0 ton and buy all 10 tons (20,000 lbs) 6 months from now as per the prevailing prices then

20,000 pounds as per the price schedule

There are 5 possible prices

• cost= 0.078*20000 = $1,560

• cost= 0.083*20000 = $1,660

• cost= 0.087*20000 = $1,740

• cost= 0.091*20000 = $1,820

• cost= 0.096*20000 = $1,920

Since the optimum solution is to minimize the cost, ??for Maxmin approach we take minmax approach and for maxmax we take minmin approach

The maximum profit/minimum cost = $1,560

Minimum profit/maximum cost = $1,920

Assuming V(price) = payoff/cost of 10 tons of sugar at the price and P(price) = probability of that price

The expected value is calculated as

Now we answer the questions

Q8) Since the best decsion is to minimize the cost we will use minmax for the Maxmin method

We want the alternative which will minimize the maximum payoff

The maximum payoffs (maximum costs) of the 3 alternatives are

Decision alternatives	Minimum profit (maximum cost/payoff)
Buy the futures contract for 5 tons	$                1,876.00
Buy the futures contract for 10 tons	$                1,812.00
Buy the futures contract for 0 ton	$                1,920.00

The alternative which minimizes the maximum cost is to Buy the futures contract for 10 tons

ans: Buy the futures contract for 10 tons.

Q9) Since the optimum decision is to minimize the cost, the Maxmax method is minmin approach for us

That is we want the decsion alternative which with smallest payoff or minumum cost

The following table shows the minimum payoff for the 3 alternatives

Decision alternatives	Maximum profit (minimum cost/payoff)
Buy the futures contract for 5 tons	$                1,696.00
Buy the futures contract for 10 tons	$                1,812.00
Buy the futures contract for 0 ton	$                1,560.00

The decsion alternative with minimum cost/smallest payoff (maximim profit) is to Buy the futures contract for 0 ton (as the cost is the lowest in the above table)

ans: Buy the futures contract for 0 ton

Q10) There is no uncertainty invloved when we buy futures contract for 10 tons at Today's price.

The expected cost of buying the futures contract for 10 tons is $1,812

Q11) The expected cost (EV) of buying the futures contract for 5 tons now is $1,793 (as calculated before)

Q12) The expected cost of not buying the futures contract is $1,754

Q13) the best alternative is the one with smallest expected cost. We can see that the expected cost of not buying the futures contract is the smallest

The best decision alternative by the expected value method is

ans: Buy the futures contract for 0 ton