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

This course distills the essentials of Python's math module, focusing on trigonometric functions, logarithmic operations, and mathematical constants. Learners will gain hands-on experience using Python to perform these standard mathematical computations, ideal for beginners seeking practical skills with the math module.

Challenge: Maximizing Profit Using Quadratic Functions

Solution