from sympy import symbols, Eq, solve, diff

Define the variables and the revenue and production cost equations

x = symbols('x') # Production units y = symbols('y') # Revenue/Cost

Revenue and cost models for Option A

revenue_eq = Eq(y, -0.01 * x**2 + 1.9 * x + 1.2) cost_eq = Eq(9 * y, 11 * x - 5)

Find maximum revenue by calculating the vertex of the quadratic equation

revenue_expr = -0.01 * x**2 + 1.9 * x + 1.2 max_revenue_x = solve(diff(revenue_expr, x), x)[0] max_revenue_y = revenue_expr.subs(x, max_revenue_x)

Find breakeven points where revenue equals cost

cost_expr = (11 * x - 5) / 9 breakeven_eq = Eq(revenue_expr, cost_expr) breakeven_points = solve(breakeven_eq, x)

Profit equation

profit_expr = revenue_expr - cost_expr max_profit_x = solve(diff(profit_expr, x), x)[0] max_profit_y = profit_expr.subs(x, max_profit_x)

Convert results to thousand pesos

results = { "Max Revenue (x)": max_revenue_x.evalf(), "Max Revenue (y)": max_revenue_y.evalf(), "Breakeven Points (x)": [point.evalf() for point in breakeven_points], "Max Profit (x)": max_profit_x.evalf(), "Max Profit (y)": max_profit_y.evalf() } results{'Max Revenue (x)': 95.0000000000000, 'Max Revenue (y)': 91.4500000000000, 'Breakeven Points (x)': [-2.49809155300835, 70.2758693307861], 'Max Profit (x)': 33.8888888888889, 'Max Profit (y)': 13.2401234567901}{'Max Revenue (x)': 95.0000000000000, 'Max Revenue (y)': 91.4500000000000, 'Breakeven Points (x)': [-2.49809155300835, 70.2758693307861], 'Max Profit (x)': 33.8888888888889, 'Max Profit (y)': 13.2401234567901}successHere are the computed results for Option A:

1. Maximum Revenue:

   • Production Units (x): 95.0
   • Revenue (y): 91.45 thousand pesos

2. Breakeven Points (x):

   • Breakeven at production units: -2.50 (not feasible in this context)
   • Breakeven at production units: 70.28

3. Maximum Profit:

   • Production Units (x): 33.89
   • Profit (y): 13.24 thousand pesos

Let me know if you would like to dive deeper into any of these values, or if you'd like computations or graphs for better visualization!

Expanding Questions:

1. Would you like a detailed graph showing revenue, cost, and profit curves?
2. Should I explain how breakeven points and maximum profit were derived in more depth?
3. Do you want to calculate and compare profits at different production levels?
4. Would you like additional analysis on feasible breakeven points?
5. Should I explore other options (B, C, D) for comparative insights?

Tip:

Always validate whether breakeven points are feasible in the context of the problem to ensure accurate conclusions!