Question

blaymount amateur dramatic society is staging a play and wants to know how much to spend on advertising. its objective is to attract as many people as possible, up to the hall capacity. for the past 11 productions their spending on advertising (in hundreds of pounds) and total audience are shown in the following table. if the hall capacity is now 300 people, how much should blaymount spend on advertising?

Answer 1

Based on the historical data and the average cost per person, Blaymount should spend approximately £477 on advertising to attract as many people as possible up to the hall capacity.

To determine the relationship between spending on advertising and audience size, you can create a scatter plot in Excel. Before doing that, let's calculate the average cost per person for each production:

Average Cost per Person= Spending/Audience​ ×100

Here's the calculation for each production:

`\text{Production 2:} & \quad (5)/(250) * 100 = 2 \\\text{Production 3:} & \quad (1)/(75) * 100 = 1.33 \\\text{Production 4:} & \quad (7)/(425) * 100 = 1.65 \\\text{Production 5:} & \quad (2)/(125) * 100 = 1.6 \\\text{Production 6:} & \quad (4)/(300) * 100 = 1.33 \\`
`\text{Production 7:} & \quad (4)/(225) * 100 = 1.78 \\\text{Production 8:} & \quad (2)/(200) * 100 = 1 \\\text{Production 9:} & \quad (6)/(300) * 100 = 2 \\\text{Production 10:} & \quad (6)/(400) * 100 = 1.5 \\\text{Production 11:} & \quad (4)/(275) * 100 = 1.45 \\\end{align*} \]`

Now, let's calculate the average cost per person across all productions:

`\[ \text{Average Cost per Person} = \frac{\text{Total Spending}}{\text{Total Audience}} * 100 \]`

`\[ \text{Average Cost per Person} = ((3 + 5 + 1 + 7 + 2 + 4 + 4 + 2 + 6 + 6 + 4))/((200 + 250 + 75 + 425 + 125 + 300 + 225 + 200 + 300 + 400 + 275)) * 100 \]`

`\[ \text{Average Cost per Person} \approx 1.59 \]`

Now, you can use this average cost per person to estimate the spending needed to attract the hall capacity audience of 300 people:

`\[ \text{Estimated Spending} = \text{Average Cost per Person} * \text{Hall Capacity} \]\[ \text{Estimated Spending} \approx 1.59 * 300 \]\[ \text{Estimated Spending} \approx 477 \]`

So, based on the historical data and the average cost per person, Blaymount should spend approximately £477 on advertising to attract as many people as possible up to the hall capacity.

Question

Blaymount Amateur Dramatic Society is staging a play and wants to know how much to spend on advertising. Its objectives is to attract as many people as possible, up to the hall capacity. For the past 11 productions their spending on advertising (in hundreds of pounds) and total audience are shown in the following table. If the hall capacity is now 300 people, how much should Blaymount spend on advertising. Can you also show how answer looks like in excel graph.

Spending 3 5 1 7 2 4 4 2 6 6 4

Audience 200 250 75 425 125 300 225 200 300 400 275