A theatre records the total revenue from three group ticket sales. Let $a$ $s$ and $c$ be the prices, in dollars, of one adult, student and child ticket, respectively. The records are shown in Figure 1.

For a later performance, the regular adult ticket price is $p$ dollars. If the discount is $d$ dollars, the estimated number of discounted adult tickets sold is $4d+12$ The revenue from these tickets is modelled by

$$R=(p-d)(4d+12),$$

where $0<d<p$