1. The Five Step Method a. Ask the question b. Select the modeling approach c. f

Question

1. The Five Step Method

a. Ask the question

b. Select the modeling approach

c. formulate the model

d. solve the model

e. answer the question

The Pig Problem. A pig weighing 200 pounds gains 5 pounds per day and costs 45 cents a day to keep. The mortket price for pigs is 65 cents per pound, but is falling 1 cent per day. When should the pig be sold?

2.  Use formula P = P () (1 + R/k)^ kt where r= interest rate k= compounding frequency per year t= time in yeras p() = initial amount of money

A $50 Series EE U.S. Government Bond compounding quarterly was issued on 5-16-01 with a P () = present value = initial amount of $25.

If the value was $38 on 8-23-10, what is the interest rate?

When will the bond be valued at $50?

Estimate the doubling time with the Rule of 72.

Explanation / Answer

1)

Let the pig be sold after x days.

The weight of the pig after x days: 200+5*x

Cost of keeping the pig: 45*x cents

Market price of the pig after x days: (65-1*number of days kept)*weight of pig = (65-x)*(200+5*x) = 13000+125*x-5*x2

The profit on the pig P is : cost of selling - cost of keeping = 13000+125*x-5*x2-45*x = 13000+80*x-5*x2

The profit function reaches its extreme when its derivative is 0 and that extremum is a maxima if the second derivative at that x is negative.

P'(x) = 0 , -10*x+80 = 0 , x = 8  

At x = 8 , P"(8) = -10 , so at x = 8 we have a maxima.

The pig should be sold after 8 days to gain maximum profit.

2)

P() = 25 , k = 4 as it is compunded quarterly, time t is from 5-16-01 to 8-23-10 which is 9 years 3 months 7 days = 9.27123 years

Using the equation: 38 = 25*(1+R/4)4*9.27123 , solving for R gives R = 0.045418 per year.

The bond will be valued at 50, when: 50 = 25*(1+0.045418/4)4*t , solving for t gives t = 15.347988 years or 15 years 4 months 7 days.

The bond will be of dollar 50 at 9-23-16.

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