Northwest California Ventures Ltd. has decided to provide capital in five market areas for the start-ups. The investment consultant for the venture capital company has projected an annual rate of return based on the market risk, the product, and the size of the market.
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Market AreaAnnual Rate of Return on Capital (%)
Electronics12
Software18
Logistics15
Education12
Retail17
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The maximum capital provided will be $5 million.
The consultant has imposed conditions on allotment of capital based on the risk involved in the market.
• The capital provided to retail should be at most 40 percent of the total capital.• The capital for education should be 26 percent of the total of other four markets (Electronics, Software, Logistics, and Retail)• Logistics should be at least 15 percent of the total capital.• The capital allocated for Software plus Logistics should be no more than the capital allotted for Electronics.• The capital allocated for Logistics plus Education should not be greater than that allocated to Retail.
Calculate the expected annual rate of return based on the allocation of capital to each market area to maximize the return on capital provided. Also, show the allocation of capital for each market area.
What will be an ideal response?
Let x1 = investment on Electronics
x2 = investment on Software
x3 = investment on Logistics
x4 = investment on Education
x5 = investment on Retail
Max 0.12x1 + 0.18x2 + 0.15x3 + 0.12x4 + 0.17x5
s.t.
x5? 0.4(5,000,000)
x4 = 0.26 (x1 + x2 + x3 + x5)
x3? 0.15(5,000,000)
x2 + x3£x1
x3 + x4£x5
x1+ x2 + x3 + x4+ x5 = 5,000,000
x1, x2, x3, x4, and x5? 0
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The expected annual rate of return based on the allocation of capital to each of the five market areas, as shown below, is obtained as $736,547.62, approximately.
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| Market Area | Allocation (approx.) |
| Electronics (x1) | $984,127 |
| Software (x2) | $234,127 |
| Logistics (x3) | $750,000 |
| Education (x4) | $1,031,746 |
| Retail (x5) | $2,000,000 |
| Total | $5,000,000 |
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