import unittest
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from matplotlib.collections import PathCollection
import user_code  # Ð²Ð¸ÐºÐ¾Ð½ÑÑ ÐºÐ¾Ð´ ÐºÐ¾ÑÐ¸ÑÑÑÐ²Ð°ÑÐ°

def _dynamic(tc, ok, ok_msg, fail_msg):
    tc._testMethodName = ok_msg if ok else fail_msg
    (tc.assertTrue if ok else tc.fail)(tc._testMethodName)

A, B, C = -1, 12, -20
XV_EXPECT, MP_EXPECT = 6.0, 16.0
ROOTS_EXPECT = (2.0, 10.0)
DELTA = 1e-6

class TestProfitCompact(unittest.TestCase):

    def test_standard_checks(self):
        reasons = []

        # coefficients present & correct
        a, b, c = getattr(user_code, 'a', None), getattr(user_code, 'b', None), getattr(user_code, 'c', None)
        if (a, b, c) != (A, B, C):
            reasons.append(f"coeffsâ (-1,12,-20), got {(a,b,c)}")

        # x,y arrays correct
        x = getattr(user_code, 'x', None)
        y = getattr(user_code, 'y', None)
        if not (isinstance(x, np.ndarray) and x.size == 100 and abs(x.min())<1e-9 and abs(x.max()-12.0)<1e-9):
            reasons.append("x must be linspace(0,12,100)")
        if not (isinstance(y, np.ndarray) and isinstance(x, np.ndarray) and np.allclose(y, A*x**2 + B*x + C, atol=1e-8)):
            reasons.append("y must equal a*x**2 + b*x + c")

        # plot elements present
        ax = plt.gca()
        lines = {ln.get_label(): ln for ln in ax.get_lines() if isinstance(ln, Line2D)}
        if "Profit Function" not in lines:
            reasons.append("missing line 'Profit Function'")
        if not (ax.get_xlabel()=="Units Sold" and ax.get_ylabel()=="Profit ($1000)" and ax.get_title()=="Profit Maximization Analysis"):
            reasons.append("labels/title incorrect")

        _dynamic(self, len(reasons)==0, "PASS: standard checks", "FAIL: " + "; ".join(reasons))

    def test_optimal_units_vertex(self):
        reasons = []
        xv = getattr(user_code, 'x_vertex', None)
        mp = getattr(user_code, 'max_profit', None)
        if not (xv is not None and abs(xv - XV_EXPECT) < DELTA):
            reasons.append(f"x_vertex {xv} â  {XV_EXPECT}")
        if not (mp is not None and abs(mp - MP_EXPECT) < DELTA):
            reasons.append(f"max_profit {mp} â  {MP_EXPECT}")

        # optional: vertex marker at correct point if plotted
        ax = plt.gca()
        scatters = {c.get_label(): c for c in ax.collections if isinstance(c, PathCollection)}
        sc_v = scatters.get("Max Profit")
        if sc_v is not None:
            ok = sc_v.get_offsets().shape[0] >= 1 and np.allclose(sc_v.get_offsets()[0], [xv, mp], atol=DELTA)
            if not ok:
                reasons.append("vertex marker not at (x_vertex, max_profit)")

        _dynamic(self, len(reasons)==0, "PASS: optimal units (vertex) correct",
                 "FAIL: " + "; ".join(reasons))

    def test_breakeven_points(self):
        reasons = []

        disc = getattr(user_code, 'discriminant', None)
        if not (disc is not None and abs(disc - 64.0) < DELTA):
            reasons.append(f"discriminant {disc} â  64")

        x1 = getattr(user_code, 'x1', None)
        x2 = getattr(user_code, 'x2', None)
        roots_user = tuple(sorted([x1, x2])) if (x1 is not None and x2 is not None) else None
        if not (roots_user and np.allclose(roots_user, sorted(ROOTS_EXPECT), atol=DELTA)):
            reasons.append(f"roots {roots_user} â  {sorted(ROOTS_EXPECT)}")

        be = getattr(user_code, 'breakeven_points', None)
        if not (isinstance(be, tuple) and len(be)==2 and np.allclose(sorted(be), sorted(ROOTS_EXPECT), atol=DELTA)):
            reasons.append(f"breakeven_points {be} â  {ROOTS_EXPECT}")

        # optional: markers at y=0 for both roots
        ax = plt.gca()
        scatters = {c.get_label(): c for c in ax.collections if isinstance(c, PathCollection)}
        sc_be = scatters.get("Breakeven Points")
        if sc_be is not None:
            offs = np.array(sc_be.get_offsets())
            ok = offs.shape[0] >= 2 and np.allclose(np.sort(offs[:,0]), sorted(ROOTS_EXPECT), atol=DELTA) and np.allclose(offs[:,1], 0.0, atol=1e-9)
            if not ok:
                reasons.append("breakeven markers not at y=0 and x=2,10")

        _dynamic(self, len(reasons)==0, "PASS: breakeven points correct",
                 "FAIL: " + "; ".join(reasons))


test_code.py

Master the mathematical foundations essential for data science. Explore core concepts in functions, calculus, linear algebra, probability, and dimensionality reduction. Build both theoretical understanding and practical coding experience to strengthen your ability to analyze data, model complex systems, and apply advanced techniques in machine learning.

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Challenge: Maximizing Profit Using Quadratic Functions

Solution

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Challenge: Maximizing Profit Using Quadratic Functions

Solution