Question 1:
The Metal Discovery Group (MDG) is a company set up to conduct geological explorations of parcels of land to ascertain whether significant metal
deposits (worthy of further commercial exploitation) are present or not. Current MDG has an option to purchase outright a parcel of land for 3 million
AED.
If MDG purchases this parcel of land, then it will conduct a geological exploration of the land. Experience indicates that for the type of parcel of land
under consideration geological explorations cost approximately 1 million AED and yield significant metal deposits as follows:

• manganese 1% chance
• gold 0.05% chance
• silver 0.2% chance
  Only one of these three metals are ever found (if at all), i.e. there is no chance of finding two or more of these metals and no chance of finding any
  other metal.
  If manganese is found then the parcel of land can be sold for 30 million AED, if gold is found then the parcel of land can be sold for 250 million AED
  and if silver is found the parcel of land can be sold for 150 million AED.
  MDG can, if they wish, pay 0.75 million AED for the right to conduct a three-day test exploration before deciding whether to purchase the parcel of
  land or not. Such three-day test explorations can only give a preliminary indication of whether significant metal deposits are present or not and
  experience indicates that three-day test explorations cost 0.25 million AED and indicate that significant metal deposits are present 50% of the time.
  If the three-day test exploration indicates significant metal deposits then the chances of finding manganese, gold and silver increase to 3%, 2% and
  1% respectively. If the three-day test exploration fails to indicate significant metal deposits then the chances of finding manganese, gold and silver
  decrease to 0.75%, 0.04% and 0.175% respectively.
  a) What would you recommend MDG should do and why?
  b) A company working in a related field to MDG is prepared to pay half of all costs associated with this parcel of land in return for half of all revenues.
  Under these circumstances what would you recommend MDG should do and why?

Question 2:

The Battery Park Stable feeds and houses the horses used to pull tourist-filled carriages through the streets of Charleston’s historic waterfront area.
The stable owner, an ex-racehorse trainer, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he would like to
keep the overall daily cost of feed to a minimum.

The feed mixes available for the horses’ diet are an oat product, a highly enriched grain, and a mineral product. Each of these mixes contains a certain
amount of five ingredients needed daily to keep the average horse healthy. The below table shows these minimum requirements, units of each
ingredient per pound of feed mix, and costs for the three mixes.

In addition, the stable owner is aware that an overfed horse is a sluggish worker. Consequently, he determines that a total of 6 pounds of feed per day
is the most that any horse needs to function property.

DIET REQUIREMENT (INGREDIENTS) FEED MIX

OAT PRODUCT (UNITS/LB) ENRICHED GRAIN (UNITS/LB) MINERAL PRODUCT (UNITS/LB) MINIMUM DAILY REQUIREMENT (UNITS)
A2316

B051052

C3569

D11528

E0505155

Cost/lb 9 1417

Formulate this LP problem and solve for the optimal daily mix of the three feeds.

Question 3:

{Investment decision problem) The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 of her money
obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own
ideas about the distribution of the funds being invested. In particular, she requests that the firm select what- ever stocks and bonds they believe are
well rated but within the following guidelines:

@e Municipal bonds should constitute at least 20% of the investment.

ee At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers.

ee No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high-yield nursing home stock.

Subject to these restraints, the client’s goal is to max- imize projected return on investments. The analysts at Heinlein and Krampf, aware of these
guidelines, prepare a list of high-quality stocks and bonds and their corresponding rates of return:

INVESTMENT PROJECTED RATE OF RETURN (%)

Los Angeles municipal bonds 5.3

Thompson Electronics 6.8

Inc. United Aerospace Corp 4.9

Palmer Drugs 8.4

Happy Days Nursing Homes 11.8

(a) Formulate this portfolio selection problem using LP.

(b) Solve this problem.