Question: 4. (20 points) Daniel Plainview operates a mid-sized oil drilling firm based out of Midland, TX. Mr. Plainview has hired your consulting firm (at significant

4. (20 points) Daniel Plainview operates a

4. (20 points) Daniel Plainview operates a mid-sized oil drilling firm based out of Midland, TX. Mr. Plainview has hired your consulting firm (at significant expense) to help him maximize his profit from his current oil fields over the next month. Currently, he's able to recover two types of oil products from his wells: crude oil and natural gas. Crude oil and natural gas respectively yield profits of $50 per gallon and $10 per cubic foot. It takes 1 hour of labor to recover a gallon of crude oil and 30 minutes of labor to recover a cubic foot of natural gas. Mr. Plainview will have 10,000 labor hours available. The wells can produce a maximum of 4000 gallons of crude oil and 15,000 cubic feet of natural gas. What mix of crude oil and natural gas would you recommend to Mr. Plainview? a. (10 Points) Mathematically formulate Mr. Plainview's problem. YOU MAY HANDWRITE AND SCAN THIS, BUT IT MUST BE INCLUDED IN THE PDF SUBMISSION. b. (7 points) Formulate and solve Mr. Plainview's problem in MS Excel. c. (3 Points) What possible assumptions do you find unrealistic? Are all the quantities here really non-random? (There are many possible answers to this question. Be creative!)

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