`S(P) =1/2P + 40`
`D(P) = 220-P`
The quantity of a product supplied and the quantity of the product demanded in an economic market are functions of the price of the product. The functions above are the estimated supply and demand functions for a certain product. The function S P( ) gives the quantity of the product supplied to the market when the price is P dollars, and the function D P( ) gives the quantity of the product demanded by the market when the price is P dollars.
How will the quantity of the product supplied to the market change if the price of the product is increased by $10 ?

Options

A. The quantity supplied will decrease by 5 units
B. The quantity supplied will increase by 5 units.
C. The quantity supplied will increase by 10 units.
D. The quantity supplied will increase by 50 units.

Answer

To solve the problem, we need to analyze how the supply function changes when the price of the product is increased by $10.

### Step-by-Step Solution:

1. **Identify the Supply Function**:
The supply function is given as:
\[ S(P) = \frac{1}{2}P + 40 \]

2. **Define the Initial Price**:
Let the initial price be \( P = x \). Therefore, the quantity supplied at this price is:
\[ S(x) = \frac{1}{2}x + 40 \]

3. **Increase the Price by $10**:
If the price is increased by $10, the new price becomes:
\[ P = x + 10 \]

4. **Calculate the New Supply Quantity**:
Substitute \( P = x + 10 \) into the supply function:
\[ S(x + 10) = \frac{1}{2}(x + 10) + 40 \]

5. **Simplify the New Supply Quantity**:
\[ S(x + 10) = \frac{1}{2}x + \frac{1}{2}(10) + 40 \]
\[ S(x + 10) = \frac{1}{2}x + 5 + 40 \]
\[ S(x + 10) = \frac{1}{2}x + 45 \]

6. **Determine the Change in Supply**:
Now, we find the change in supply by subtracting the initial supply from the new supply:
\[ \text{Change in Supply} = S(x + 10) - S(x) \]
\[ \text{Change in Supply} = \left(\frac{1}{2}x + 45\right) - \left(\frac{1}{2}x + 40\right) \]
\[ \text{Change in Supply} = 45 - 40 = 5 \]

### Conclusion:
When the price of the product is increased by $10, the quantity of the product supplied to the market increases by **5 units**.