Choose a feasible portfolio
Independent, mutually exclusive, and interdependent projects describe which combinations can actually be implemented.
| Portfolio | Cost ($k) | Total PW ($k) | Feasible |
|---|---|---|---|
| None | 0 | 0 | Yes |
| A | 10 | 7 | Yes |
| B | 15 | 10 | Yes |
| C (requires A) | 18 | 13 | Yes |
| A+B | 25 | 17 | No |
| A+B+C | 33 | 23 | No |
Best feasible portfolio: C (requires A). A costs 10 and yields PW 7; B costs 15; C costs 8 and adds PW 6 but requires A.
Independent A and B may both be chosen if the budget permits.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
What the model means
Independent projects may coexist. Mutually exclusive projects cannot both be chosen. An interdependent project can require another project, or a package may have benefits different from the sum of its individual parts. Budget constraints apply to the chosen combination.
Build the calculation
For binary selections x_j, a budget is ΣI_jx_j≤B; exclusivity is x_A+x_B≤1; a requirement C⇒A is x_C≤x_A. Enumerate feasible combinations for small cases, calculate total PW, and select the best feasible package. The illustrative model assumes additive PW within allowed packages.
Set up. Calculate. Explain.
Rebuild the starting scenario
Budget: 20 $ thousand; PW of project B: 10 $ thousand. Calculate the largest feasible portfolio present worth.
Setup hint
Independent A and B may both be chosen if the budget permits.
Open the visual solution
- Independent A and B may both be chosen if the budget permits.
- Interdependency C ⇒ A imposes x_C ≤ x_A. Mutually exclusive alternatives would impose x_A+x_B≤1 instead.
- Enumerate feasible combinations and maximize total PW under the budget; highest standalone return is not enough.
| Portfolio | Cost ($k) | Total PW ($k) | Feasible |
|---|---|---|---|
| None | 0 | 0 | Yes |
| A | 10 | 7 | Yes |
| B | 15 | 10 | Yes |
| C (requires A) | 18 | 13 | Yes |
| A+B | 25 | 17 | No |
| A+B+C | 33 | 23 | No |
Best feasible portfolio: C (requires A). A costs 10 and yields PW 7; B costs 15; C costs 8 and adds PW 6 but requires A.
Independent A and B may both be chosen if the budget permits.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Transfer the idea to a new scenario
Use a $26k budget and PW(B)=$11k in the displayed portfolio. A costs $10k with PW $7k; C costs $8k with PW $6k and requires A. Find the best feasible total PW.
Setup hint
Independent A and B may both be chosen if the budget permits.
Open the visual solution
- Independent A and B may both be chosen if the budget permits.
- Interdependency C ⇒ A imposes x_C ≤ x_A. Mutually exclusive alternatives would impose x_A+x_B≤1 instead.
- Enumerate feasible combinations and maximize total PW under the budget; highest standalone return is not enough.
| Portfolio | Cost ($k) | Total PW ($k) | Feasible |
|---|---|---|---|
| None | 0 | 0 | Yes |
| A | 10 | 7 | Yes |
| B | 15 | 11 | Yes |
| C (requires A) | 18 | 13 | Yes |
| A+B | 25 | 18 | Yes |
| A+B+C | 33 | 24 | No |
Best feasible portfolio: A+B. A costs 10 and yields PW 7; B costs 15; C costs 8 and adds PW 6 but requires A.
Independent A and B may both be chosen if the budget permits.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
If C can be implemented only with A, which constraint expresses it?
Can you defend your setup?
Can you place each amount on the timeline, match the interest period, calculate the equivalent quantity, and state the decision or limitation?
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