SUBJECT - OPERATIONS MANAGEMENT

** PROVIDE CORRECT SOLUTION OF ALL THE QUESTIONS**

A portfolio manager must determine how to allocate the portfolio's funds. There are five investments under consideration, bonds, mutual funds, ETFs, Real Estate, and Gold. The expected return from the investments are 2%, 5%, 8%, 12%, and 3%, respectively. a. Construct the portfolio that results in the highest expected return if we have the following requirements: i) at least 10% of our portfolio must be gold, ii) no more than 20% of the portfolio can be real estate, ii) at least 25% must be in a combination of mutual funds and ETFs, iv) the amount invested in mutual funds must be at least as much as is invested in ETFs, and v) we must have more in bonds than we have in a combination of Real Estate and Gold. The remaining parts of this problem also require the following information: Mutual Fund -0.3 Real Estate ETF 0.2 Covariance Bonds Mutual Fund ETF Real Estate -0.4 0.7 Gold 0.05 0.02 -0.05 -0.1 -0.15 0.4 Varianc e 0.005 Investment Bonds Mutual Fund ETF Real Estate Gold 0.02 0.04 0.05 0.0075 b. Construct a mean-variance model that minimizes variance while guaranteeing an expected return of at least 8%. C. Construct a mean-variance model that maximizes expected return while holding the variance below 0.01. d. Construct a mean-variance model that maximizes expected return while holding the variance below 0.01 and meeting requirements i, ii, and is from part a. 42 43 20. A teller at a drive-up window at a bank had the following service times (in minutcs) for 20 ran- domly selected customers. SAMPLE 1 2 3 4.5 4.6 4.5 4.7 42 4.5 4.6 4.6 4.4 4.8 4.3 4.7 4.4 4.5 4.3 4.6 4.9 1. Determine the mean of cach sample. b. I the prxcess parameters are unknown, estimate its mean and standard deviation. c. Estimate the mean and standard deviation of the sampling distribution. d. What would three-sigma control limits for the process be? What alpha risk would they provide c Wut alpha risk would central limits of 4.14 and 1.86 provide r. Using limits of 4.11 and 4.86, are any sample means beyond the control lmits? If so, which one's)? 3. Construct control clarts for means and ranges using Table 10.3. Are any samples beyond the control limits? If so, which one(s)? h. Explain why the controllimits are different fier means in parts dando 1. If the process has a known mean of 4.4 and a known standard deviation of 18, what would dlaree-sigm controllimits he for a man chart: Ar any simple means beyond the controllim- is? I' so, which ente(s): CS scanned with CamScanner