# Simulation using analytic solver platform

Assignments: It is strongly recommended that you create a separate file for each of these problems in order to avoid that the simulation runs interfere with each other. For all problems, run 5000 trials.

Solve the following problems in Excel using Excel add-in- ‘analytical solver platform’ (due Thursday, oct 29th)

Q. 11. The owner of a ski apparel store in Winter Park, Colorado must make a decision in July regarding the number of ski jackets to order for the following ski season. Each ski jacket costs \$54 each and can be sold during the ski season for \$145. Any unsold jacket at the end of the season are sold for \$45. The demand for jackets is expected to follow a Poisson distribution with an average rate of 80. The store owner can order jackets in lot sizes of 10 units.

a. How many jackets should the store owner order if she wants to maximize her expected profit?

b. What are the best-case and worst-case outcomes the owner may face on this product if she implements your suggestion?

c. How likely is it that the store owner will make at least \$7,000 if she implements your suggestion?

d. How likely is it that the store owner will make between \$6,000 and \$7,000 if she implements your suggestion?

Hints:

a.    Solve as a combination of simulation/optimization. The following functions will help with this problem (you may need others also which you have used before): PsiPoisson (see page 577) Psimin and Psimax (see pages 602-603); Psitarget (see page 596). 17 pts

b.     Solve without an optimization. Instead, build a model and vary the order quantity in between 50, 60, 70, 80, 90, 100, 110  using the PsiSimParam function as discussed in section 12.14.2. Create a table similar to Figure 12.22. Answer all questions and discuss in case you find differences to your solution in part a). 15 pts

Q.17. Lynn Price recently completed her MBA and accepted a job with an electronics manufacturing company. Although she lilkes her job, she is also looking forward to retiring one day. To ensure that her retirement is comfortable, she intends to invest \$3,000 of her salary into a tax-sheltered retirement fund at the end of each year. Lynn is not certain what rate of return this investment will earn each year, but she expects each year’s rate of return could be modeled appropriately as a normally distributed random variable with a mean of 12.5% and standard deviation of 2%.

a. If Lynn is 30 years old now, how much money should she expect to have in her retirement fund at age 60?

b. Construct a 95% confidence interval for the average amount Lynn will have at age 60.

c. What is the probability that Lynn will have more than \$1 million in her retirement fund when she reaches age 60?

d. How much should Lynn invest each year if she wants there to be a 90% chance of having at least \$1 million in her retirement fund at age 60?

e. Suppose Lynn contributes \$3,000 annually to her retirement fund for eight years and then terminates her annual contributions. How much of her salary would she have contributed to this retirement plan and how much money could she expect to have accumulated at age 60?

f. Now suppose that Lynn contributes nothing to her retirement fund for eight years and then begins contributing \$3,000 annuallly until age 60. How much of her salary would she have contributed to this retirement plan, and how much money could she expect to have accumulated at age 60?

g. What should Lynn (and you) learn from the answers to questions e and f?

Hints:  Part d) is similar to last week – try different values, explain what you did and provide answers. Show a new model for e) and f. 25 pts. For the interest calculation, assume that there is no interest in the first year (when she is 30) just the addition of \$3000. Year “60” is the last year where funds and interest are added.

Note : All solutions need to be done in excel using ‘Analytical solver platform’.

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