Optimize profitability for coding contract decisions

A client offers two mutually exclusive fixed-price projects starting 2025-10-01 with a hard deadline of 2025-10-31. Your current team has 3 engineers. Costs and productivity: • Base pay cost: $70/hour/engineer; overhead 25% on labor cost. • Regular hours: up to 40 hrs/week/engineer at 25 lines/hour. • Overtime: up to 20 hrs/week/engineer at 1.5x pay; productivity on overtime is 20 lines/hour. • Optional contractor: $110/hour, 22 lines/hour, 10 hours of onboarding at 50% productivity; no overtime; 10% agency fee on contractor labor cost. Quality: 8% of produced lines require rework (same productivity, unpaid by client), discovered within the month. Client options: • Project A: 1,000 lines; pays $45/line; on-time bonus $5,000; late penalty $3,000 per week. • Project B: 2,000 lines; pays $40/line; on-time bonus $12,000; same penalty. Assume workdays are evenly spread across the month and rework must also be completed by 2025-10-31 to qualify for the bonus. a) Under current staff only (no contractor), compute completion time and total profit for A and B with and without overtime (state assumptions on allocating overtime). b) If you can add one contractor starting 2025-10-07, recompute completion time and profit for A and B (include onboarding and agency fee). c) Which option maximizes expected profit while meeting the deadline with ≥95% buffer against ±10% productivity variance? d) Derive the break-even pay-per-line for Project B at which B becomes preferable to A under the best staffing plan. e) Sensitivity: how does profit change if rework rate ranges from 0% to 15%? Show formulas and final numeric recommendations.