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## Statistics

problem 1: A lobster catcher spends \$12 500 per month to maintain a lobster boat. He plans to catch an average of 20 days per month during lobster season. For each day, he should allow around \$95 for fuel and ice for the boat. If his packaging and distribution costs are \$2.00 per kilogram of lobster, and if lobster sells for \$6.00 per kilogram: (Excel is not required for this problem: Just Type your answer with appropriate steps)

a) How many kilograms of lobster should he catch per day to break even?
b) Assume that the catcher wants to put away money to sustain him via inclement weather and off-season expenses. He decides that he would like to save \$10 000 per month. How much lobster must he plan to catch to make this plan possible?

problem 2: The Widget Manufacturing Company should replace a widget machine, and is evaluating the capabilities of two systems.  A requirement of management is that the machine chosen should be paid for during the first year of operation. The first machine under consideration, Machine A, would cost \$65 000, and has the capacity to make up to 10 000 widgets per year, with a variable cost of \$22 per widget.  The second machine, Machine B, can produce widgets in almost half the time, would cost \$72 000, but the variable cost is only \$17 per widget. Widgets sell for \$32.

A)

a) Find out the break-even point in terms of Widgets for each machine.
b) Find out the break-even point in terms of dollars for each machine.
c) If the Widget Company is anticipating a demand of 5500 units in the next year, which machine must be chosen?
d) If the demand is anticipated at 7500 units, would a different system be chosen?

B) Assume an additional Machine A is installed to make Junior Widgets. The selling price for these devices is \$12 per unit, with a variable price of \$8. Compute:

a) The BEP
b) The BEP\$
c) The profit (if any) at 24 000 units

C) At what volume would the Widget Manufacturing Company in the above problem be indifferent to a choice between the two systems?

problem 3: Consider the given linear programming problem:

Minimize: 70M + 40N

Subject to: 3M + 7N ≥ 233
10M + 2N ≥ 254
2N ≥ 54
4M  ≥ 90
M ≥ 0,  N ≥ 0

A) Solve this problem graphically.

B) Then set it up in Excel and solve it.

a) What are the values of the decision variables?
b) What is the value of the objective function?
c) What are the values of the slack or surplus variables?

problem 4: Financials Investments, a group of financial advisors and retirement planners, has been requested to give advice on how to invest \$200,000 for one of its clients. The client has stipulated that the money should be put into either stocks fund or a money market fund, and the annual return should be at least \$14,000. Other conditions associated to risk have as well been specified and the given linear program was developed to help with this investment decision:

Minimize Risk = 12S + 5M
Subject to:
S + M = 200,000 (total invest is \$200,000)
0.10S + 0.05M ≥ 14,000 (return must be at least \$14,000)
M ≥ 40,000 (at least \$40,000 must be in money market)
S, M ≥0

Where,

S = dollars invested in stock fund
M = dollars invested in money market fund

A) Solve this problem graphically (As done in the class).

B) Then set it up in Excel and solve it.

a) How much money must be invested in stock fund and in money market fund?
b) What is the Total Risk?
c) What is the total return? What rate of return is this?
d) Would solution change if risk measure for each dollar in the stock fund were 14 rather than 12?
e) For each additional dollar that is available, how much does the risk change?
f) Would solution change if the amount that should be invested in the money market fund were changed from \$40,000 to \$50,000?

problem 5: The Laser Computer Printer Company decides monthly what to produce throughout the subsequent month. They produce three kinds of printers, the Laser Rocket, the Alpha Laser and the Laser Omega, which bring those profits of \$310, \$365 and \$465, correspondingly.  The Laser Rocket needs 3 hours of assembly time, and the company always produces at least 30 units per month. The Laser Omega requires 5 hours of assembly time, and the company would like to generate at least 25 of these printers. The Alpha Laser needs only 2.5 hours of assembly time. There are 400 hours of labor available for the month. What is the combination of printers Laser must produce to maximize their profits?

a) Set up this problem as an LP problem showing the data, the objective function and constraints.
b) Make an Excel Spreadsheet that reflects your LP problem and solve.

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M92015

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