Question

the demand equation for an item currently being marketed is given by $d(q) = -0.25 cdot q^2 + 42$, where $d(q)$ is in $ that can be charged per unit, and $q$ is in thousands of units that can be sold at that price. (for example, $q = 13$ means 13,000 units can be sold.) if 6,000 units are to be sold, at what price should each be set? (be careful with units when you do your calculations!) the appropriate price = $

Explanation:

Step1: Determine the value of q

Since \( q \) is in thousands of units and we want to sell 6,000 units, we divide 6,000 by 1,000 to get \( q \). So \( q=\frac{6000}{1000} = 6 \).

Step2: Substitute q into the demand function

The demand function is \( D(q)=- 0.25\cdot q^{2}+42 \). Substitute \( q = 6 \) into the function:
\[

$$\begin{align*} D(6)&=-0.25\times(6)^{2}+42\\ &=- 0.25\times36 + 42\\ &=-9 + 42\\ &=33 \end{align*}$$

\]

Answer:

33