To determine how much more power we need to feed back into the grid to break even, we need to calculate the additional energy required so that the revenue from selling power to the grid equals the cost of buying power from the grid. Let’s break this down step by step.
Given:
– **Selling price**: The grid buys 1 kWh from us at R1.4.
– **Buying price**: We pay R4 per kWh to the grid.
– **Goal**: Break even, meaning the total cost of the energy we buy equals the total revenue from the energy we sell.
Step 1: Define the variables
– Let \( C \) be the amount of energy (in kWh) we **consume** from the grid.
– Let \( S \) be the amount of energy (in kWh) we **sell** back to the grid.
– **Cost** of energy consumed = \( C \times R4 \).
– **Revenue** from energy sold = \( S \times R1.4 \).
– Break-even condition: Cost = Revenue, so:
\[ C \times 4 = S \times 1.4 \]
Step 2: Interpret the question
The phrase “how much more power do we need to feed back into the grid to break even” suggests we’re looking for the additional energy we need to sell to offset the cost of what we consume. However, we need a starting point. A common interpretation in such problems is to assume a baseline where consumption and production are equal (e.g., 1 kWh consumed and 1 kWh sold), then calculate the extra amount needed to balance the higher buying price against the lower selling price.
Let’s assume:
– We consume 1 kWh from the grid as a baseline.
– We want to know how much total energy \( S \) we need to sell to break even, and then how much *more* than 1 kWh that is.
Step 3: Calculate for 1 kWh consumed
– Cost of 1 kWh consumed = \( 1 \times R4 = R4 \).
– Revenue from selling \( S \) kWh = \( S \times R1.4 \).
– Break-even equation:
\[ 4 = S \times 1.4 \]
– Solve for \( S \):
\[ S = \frac{4}{1.4} \]
\[ S \approx 2.857 \, \text{kWh} \]
So, to break even on 1 kWh consumed, we need to sell approximately 2.857 kWh back to the grid.
Step 4: Determine “how much more
If we start with a baseline of selling 1 kWh (a neutral point where consumption = production), we’re currently earning:
– Revenue = \( 1 \times R1.4 = R1.4 \).
– Cost = \( 1 \times R4 = R4 \).
– Net loss = \( R4 – R1.4 = R2.6 \).
To break even, we need to sell 2.857 kWh total. If we’re already selling 1 kWh, the additional amount is:
\[ 2.857 – 1 = 1.857 \, \text{kWh} \]
Step 5: Generalise the answer
Alternatively, the question might imply a ratio: for every 1 kWh consumed, how much *additional* power beyond consumption do we need to sell? From the calculation:
– Total sold = 2.857 kWh.
– Consumed = 1 kWh.
– Additional power sold beyond consumption = \( 2.857 – 1 = 1.857 \, \text{kWh} \).
Thus, for every 1 kWh consumed, we need to feed an *extra* 1.857 kWh into the grid to break even.
Final Answer:
You need to feed an additional **1.857 kWh** into the grid for every 1 kWh consumed to break even, given the grid buys at R1.4 per kWh and you pay R4 per kWh.
