Suppose you represent the Firm A and your specialty is to
analyse startups. Specifically, Firm A is looking to invest at
least $65 million (no more than $85 million) into several startup
companies and your job is to evaluate the business plan of 20
companies to determine whether they are good investments. After
performing painstaking research, you have compiled the following
table which gives the industry the startup is in, the amount of
money that would need to be invested, the expected return on that
investment, and your risk assessment (1 is the safest investment
while 10 is considered most risky).
Because investing is unpredictable, if two or more startups are
chosen in the same industry, an additional risk value of four (+4)
must be factored into the assessment. Note that the following
requirements must be met:
1) Firm A cannot invest more than 40% of its capital in any single
industry.
2) The percentage gain of the investment should exceed 33%.
Formulate and solve a binary program to minimise the sum of
risks. (Explain and give the equation of decision variables,
optimal solution, constraints; eg. one of the DV is 𝑥𝑖 = 1 if
invest in startup i; 0 otherwise, where i = 1,..., 20)
Solve the problem using the excel solver.
Startup ID Industry Investment Degree of Risk 1 Health 2 6 3 6 4 Health Health Health Tech Tech 10 5 4 6 5 7 Tech 7 8 Tech 5 9 Food 3 10 Food Expected Return $6,560,498.80 $6,780,075.00 $6,319,693.93 $9,865,219.86 $5,886,612.77 $4,650,092.00 $10,641,062.95 $6,748,642.23 $5,550,097.00 $9,333,191.81 $6,842,044.67 $9,291,426.43 $8,244,307.57 $9,512,117.90 $6,062,338.75 $7,919,594.81 $8,432,901.76 $5,437,932.00 $6,098,018.81 $5,206,554.28 $3,330,105.00 $6,117,680.23 $4,050,126.00 $5,280,131.00 $4,650,072.00 $4,526,987.16 $3,420,068.00 $3,900,129.00 $5,147,799.76 $3,540,118.00 $3,810, 107.00 $5,160,139.00 $3,750,052.00 $5,010,110.00 $4,560,143.00 $3,000,110.00 $7,380,146.00 $3,990,128.00 $4,230,112.00 $4,380,126.00 5 11 Food 9 12 2 w n 13 10 14 2 15 9 16 Food Nonprofit Nonprofit Nonprofit Nonprofit Social Media Social Media Social Media Social Media 5 17 6 18 1 19 2 20 3
Suppose you represent the Firm A and your specialty is to analyse startups. Specifically, Firm A is looking to invest at
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