DATA: https://docs.google.com/spreadsheets/d/1AwbWgj09keDs6S5N-limjOXSthXOPkAc/edit?usp=sharing&ouid=115011566029800565379&rtpof=true&sd=true

Part A

The CFO at Performance Lawn Equipment wishes to design a minimum variance portfolio of index funds to invest some of the firm's cash reserves. The table below shows the average returns and variance-covariance matrix.

Categories	Bond	S&P 500	Small Cap	Mid Cap	Large Cap	Emerging Market	Commodity
Bond	0.002%
S&P 500	-0.001%	0.020%
Small cap	-0.001%	0.027%	0.047%
Mid cap	-0.001%	0.024%	0.039%	0.033%
Large cap	-0.001%	0.019%	0.027%	0.023%	0.027%
Emerging Market	0.000%	0.032%	0.050%	0.043%	0.041%	0.085%
Commodity	0.000%	0.000%	0.005%	0.005%	0.009%	0.015%	0.054%
Average Weekly Return	0.044%	0.118%	0.256%	0.226%	0.242%	0.447%	0.053%

1. The firm would like to achieve a target return of 0.19%. What mix of investments would achieve this?
2. To obtain better diversification, the CFO would like to restrict the percentage of investments in each fund as follows. How would the optimal portfolio and objective change?
   • Bond: between 10% and 50%
   • S&P 500: between 30% and 50%
   • Small cap: no more than 20%
   • Mid cap: no more than 20%
   • Large cap: no more than 25%
   • Emerging market: no more than 10%
   • Commodity: no more than 20%

Part B

PLE produces metal engine housings from sheet metal for both mowers and tractors. Production consists of five steps: (1) stamping, (2) drilling, (3) assembly, (4) painting, and (5) packaging. The production rates are given in Table 11.2. In addition, mower housings require 1.2 square feet of sheet metal per unit, and tractor housings require 1.8 square feet per unit, and 2,500 square feet of sheet metal is available. The company would like to maximize the total number of housings they can produce during the planning period. Formulate and solve a linear optimization model using Solver and recommend a production plan. Illustrate the results visually to help explain them. Conduct whatever what-if analyses are appropriate. Summarize the results.

Department	Mower Housings	Tractor Housings	Production Hours Available
Stamping	0.03	0.07	200
Drilling	0.09	0.06	300
Assembly	0.15	0.10	300
Painting	0.04	0.06	220
Packaging	0.02	0.04	100

Complete the tasks and explain key insights. What did you learn?