subject: operation mangment

could you answer this question with explain it please

\\[ Q_{B E P}=\\frac{\\mathrm{FC}}{R-v} \\] Profit \\( (P)=\\mathrm{TR}-\\mathrm{TC}=R \\times Q-(\\mathrm{FC}+v \\times Q)=Q(R-v)-\\mathrm{FC} \\) A firm is considering three capacity alternatives: A, B, and C. Alternative A would have an annual fixed cost of \\( \\$ 100,000 \\) and variable costs of \\( \\$ 22 \\) per unit. Alternative \\( B \\) would have annual fixed costs of \\( \\$ 120,000 \\) and variable costs of \\( \\$ 20 \\) per unit. Alternative C would have fixed costs of \\( \\$ 80,000 \\) and variable costs of \\( \\$ 30 \\) per unit. Revenue is expected to be \\( \\$ 50 \\) per unit. (A) Which alternative has the lowest break-even quantity? (B) Which alternative will produce the highest profits for an annual output of 10,000 units? (C) Which alternative would require the lowest volume of output to generate an annual profit of \\( \\$ 50,000 \\) ? (D) Which alternative should I choose for a quantity of 25,000 units? (HINT: THERE ARE 2 INDIFFERENCE POINTS)