Budget Allocation Across Acquisition Channels

Context

You are given an Excel sheet with per-channel performance metrics for three acquisition channels: Phone Calls, Social Media Ads, and Email Blasts. For each channel, the sheet provides:

• Click-through rate (CTR)
• Conversion rate (CVR)
• Revenue-per-cost (RPC), i.e., expected revenue generated per $1 of spend
• An individual spend cap for that channel

If RPC is not directly provided, it can be derived from CTR, CVR, average revenue per conversion (R), and the channel's pricing model (e.g., CPM, CPC, cost per send). Assume linear returns up to each channel’s cap (no saturation within cap) and that all rates are stable over the budget range considered.

Tasks

1. Given a total budget B, compute the expected net profit for each channel if you allocate an amount s to that channel (you may consider the case where all of B is spent in a single channel, ignoring caps for this part).
2. Using the conversion rate for the Phone Calls channel, estimate:
   • The average cost per inbound phone call
   • The average profit per inbound phone call
3. Each channel has an individual spend cap. With a fixed overall budget B, determine the spending allocation across channels that maximizes total profit. Explain your reasoning.

Hints

• First compute unit profit per $1 of spend for each channel: unit profit = revenue-per-cost − 1.
• Then apply budget constraints and use a simple greedy/linear optimization to maximize profit under caps.