Final answer:
To express the total revenue R as a function of the price p per item, you can use the equation R = 10q - 0.25q^2.
Step-by-step explanation:
To express the total revenue R as a function of the price p per item, we need to find the equation that relates quantity demanded (q) and price (p). The given demand equation is q = -4p + 40. We can solve this equation for p by isolating p on one side:
p = (40 - q) / 4
Revenue (R) is calculated by multiplying the quantity (q) by the price (p). So, substituting the value of p in terms of q, we get:
R = p * q = ((40 - q) / 4) * q = 10q - 0.25q^2