A company has a budget of $10,000 to invest in two projects, A and B. Project A returns 5% profit, while Project B returns 8%. If the company invests $x in Project A, express the total profit from both projects as a function of $x$, and find the investment in Project A that maximizes the profit.

Tue, 05 May 2026 03:54:24 +0000

**How a Company Can Strategically Allocate a $10,000 Budget Between Two Investment Projects** In an era where every dollar counts and businesses seek smarter ways to grow their budgets, a common question surfaces: If a company has $10,000 to invest across two projects, how can it balance risk, return, and growth? One well-documented scenario involves funding Project A with a 5% projected profit and Project B with an 8% return. For a wise business owner, understanding how to structure such investments is key to maximizing returns without taking unnecessary risk. This piece breaks down how investing $x in Project A and the remainder in Project B shapes total profit—and reveals the optimal allocation that numbers into maximum revenue. **Understanding the Financial Framework** At the core, the investment in Project A is denoted as $x, with the remaining $ (10,000 – x) $ flowing into Project B. Return calculations follow simple proportional math:
Total profit equals:
*[Profit from A: 0.05x]* + *[Profit from B: 0.08(10,000 – x)]*
This expression forms the foundation for decision-making—turning relative risk and return into concrete figures. Algebraically simplified, total profit becomes:
Profit = 0.05x + 800 – 0.08x
Profit = 800 – 0.03x
This linear equation shows a clear trend: as investment in Project A increases, total profit diminishes linearly. The slope of –0.03 reflects the opportunity cost—every dollar redirected from B to A reduces total gains.