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[lp_intro]Update lp #531

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merged 3 commits into from
Jul 26, 2024
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[lp_intro]Update lp #531

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ca330c7
explain iso-revenue lines
longye-tian Jul 23, 2024
72e85d5
add comma in the numbers
longye-tian Jul 23, 2024
980e784
Update lectures/lp_intro.md
longye-tian Jul 23, 2024
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16 changes: 9 additions & 7 deletions lectures/lp_intro.md
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Original file line number Diff line number Diff line change
Expand Up @@ -91,6 +91,8 @@ $$

The following graph illustrates the firm's constraints and iso-revenue lines.

Iso-revenue lines show all the combinations of materials and labor that produce the same revenue.

```{code-cell} ipython3
---
tags: [hide-input]
Expand Down Expand Up @@ -335,7 +337,7 @@ OR-Tools tells us that the best investment strategy is:

3. At the beginning of the third year, the bank balance should be $ \$75,072.245 $.

4. At the end of the third year, the mutual fund will get payouts from the annuity and corporate bond and repay its loan from the bank. At the end it will own $ \$141018.24 $, so that it's total net rate of return over the three periods is $ 41.02\%$.
4. At the end of the third year, the mutual fund will get payouts from the annuity and corporate bond and repay its loan from the bank. At the end it will own $ \$141,018.24 $, so that it's total net rate of return over the three periods is $ 41.02\%$.



Expand Down Expand Up @@ -542,14 +544,14 @@ c_ex2 = np.array([1.30*3, 0, 0, 1.06, 1.30])
A_ex2 = np.array([[1, 1, 0, 0, 0],
[1, -rate, 1, 0, 1],
[1, 0, -rate, 1, 0]])
b_ex2 = np.array([100000, 0, 0])
b_ex2 = np.array([100_000, 0, 0])

# Bounds on decision variables
bounds_ex2 = [( 0, None),
(-20000, None),
(-20000, None),
(-20000, None),
( 0, 50000)]
(-20_000, None),
(-20_000, None),
(-20_000, None),
( 0, 50_000)]
```

Let's solve the problem and check the status using `success` attribute.
Expand Down Expand Up @@ -581,7 +583,7 @@ SciPy tells us that the best investment strategy is:

3. At the beginning of the third year, the mutual fund should borrow $ \$20,000$ from the bank and invest in the annuity.

4. At the end of the third year, the mutual fund will get payouts from the annuity and corporate bond and repay its loan from the bank. At the end it will own $ \$141018.24 $, so that it's total net rate of return over the three periods is $ 41.02\% $.
4. At the end of the third year, the mutual fund will get payouts from the annuity and corporate bond and repay its loan from the bank. At the end it will own $ \$141,018.24 $, so that it's total net rate of return over the three periods is $ 41.02\% $.



Expand Down