A manufacturing company makes two types of water​ skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table.

 A manufacturing company makes two types of water​ skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table.

 

Answer parts​ (A), (B), and​ (C) below.

 ​(A) If the profit on a trick ski is ​$60 and the profit on a slalom ski is ​$55​, how many of each type of ski should be manufactured each day to realize a maximum​ profit? What is the maximum​ profit?

 First use the manufacturing data to create constraints and an equation for the profit. Let x represent the number of trick skis and let y represent the number of slalom skis produced daily. The equation for the daily profit is shown below.

The feasible region is bounded. By the information​ above, both the maximum value and the minimum value of the objective function exist.

Since the maximum value of P​ exists, it must occur at one​ (or more) of the corner points of the feasible region. Find the coordinates of each corner point of the feasible region.

Thanks

A landowner in Texas is offered $200,000 for the exploration rights to oil on her land, along with a 25% royalty on the future profits if oil is discovered. The landowner is also tempted to develop the field herself, believing that the interest in her land is a good indication that oil is present.

 A landowner in Texas is offered $200,000 for the exploration rights to oil on her land, along with a 25% royalty on the future profits if oil is discovered. The landowner is also tempted to develop the field herself, believing that the interest in her land is a good indication that oil is present. In that case, she will have to contract a local drilling company to drill an exploratory well on her own. The cost for such a well is $750,000, which is lost forever if no oil is found. If oil is discovered, however, the landowner expects to earn future profits of $7,500,000. Finally, the landowner estimates (with the help of her geologist friend) the probability of finding oil on this site to be 60%.

A. Construct a decision tree to help the landowner make her decision. Make

sure to label all decision and chance nodes and include appropriate costs,

payoffs and probabilities.

The decision tree is shown below:

The initial decision is wheather to self develop the field or give it to other.

If she develops herself then she incurrs a initial cost of $750000 for oil exploration.

Then if oil is found (which has 60% probabaility), the profit will be $7500000.

Thus new profit if self developed and oil is found will be $7500000 - $750000 = $6750000.

If oil is not found then the net profit will be negative i,e, loss of $750000 (oil exploration cost).

If initially she decides to let other develop the field then:

If oil is found then total profit will be $200000 (offered for land) + 0.25 * 7500000 (25% of future profit) = $ 2075000

IF oil is not found then profit will be $200000 (offered for land)

Thus Net result for decision 1 (Self develop) = 0.6 * 6750000 + 0.4 * (-750000)

Net result =  4050000 - 300000 = $3750000

Net result for decision 2 (Let other develop) = 0.6 * 2075000 + 0.4 * 200000

Net result = 1245000 + 80000 = $1325000



Thus decision 1 is better for her as it has better payoff.