High School

We appreciate your visit to 1 A firm is developing a TV advertising campaign Development costs fixed costs are Rs 150 000 and the firm must pay Rs 15 000. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

1. A firm is developing a TV advertising campaign. Development costs (fixed costs) are Rs. 150,000, and the firm must pay Rs. 15,000 per minute for television spots. The firm estimates that for each minute of advertising, additional sales of Rs. 70,000 result. Of this Rs. 70,000, Rs. 47,500 is absorbed to cover the variable cost of producing items, and Rs. 15,000 must be paid for per minute of advertising. Any remainder is the contribution to fixed costs and profit.

(i) How many minutes of advertising are necessary to recover the development costs of the advertising campaign?

(ii) If the firm uses 15 one-minute spots, determine total revenue, total cost (production and advertising), and total profit (or loss) resulting from the campaign.

2. A car rental agency charges Rs. 15 per mile if the total mileage does not exceed 100. If the total mileage exceeds 100, the agency charges Rs. 15 per mile for the first 100 miles plus Rs. 9 per mile for the additional mileage. If \( x \) represents the number of miles a rented vehicle is driven, express the mileage charges \( C(x) \) as a function of \( x \). Find \( C(50) \) and \( C(150) \).

3. A machine costing Rs. 4,000 is estimated to have a useful life of 6 years and then to have a scrap value of Rs. 400. It is assumed that the value of the machine decreases by an equal amount by the end of every year.

(i) Find the average yearly decrease in the value of the machine.

(ii) Write an equation showing the relation of the value of the machine with the age of the machine in years.

(iii) Prepare a schedule showing the value of the machine by the age of the machine.

4. A firm sells a single product for Rs. 65 per unit. Variable costs per unit are Rs. 20 for material and Rs. 27.50 for labour. Annual fixed costs are Rs. 180,000.

(i) Construct the profit function stated in terms of \( x \), the number of units produced and sold.

(ii) What profit is earned if annual sales are 20,000 units?

5. A local university football team has added a national power to next year's schedule. The team has agreed to play the game for a guaranteed fee of Rs. 100,000 plus 25% of the gate receipts. Assume that the ticket price is Rs. 12.

(i) Determine the number of tickets that must be sold to recover the Rs. 100,000 guarantee.

(ii) If university officials hope to achieve a net profit of Rs. 240,000 from the game, how many tickets must be sold?

(iii) If a sell-out of 50,000 fans is assured, what ticket price would allow the university to earn the desired profit of Rs. 240,000?

Answer :

  1. For the advertising campaign:

    (i) To determine how many minutes of advertising are necessary to recover the development costs, we need to find when the contribution to fixed cost and profit equals the fixed costs of Rs. 150,000. The contribution per minute is calculated as follows:

    [tex]\text{Contribution per minute} = Rs. 70,000 - Rs. 47,500 - Rs. 15,000 = Rs. 7,500[/tex]

    Therefore, the number of minutes required is:

[tex]\frac{Rs. 150,000}{Rs. 7,500} = 20 \text{ minutes}[/tex]

(ii) If 15 one-minute spots are used:

  • Total revenue: [tex]15 \times Rs. 70,000 = Rs. 1,050,000[/tex]
  • Total cost (production and advertising):

[tex]15 \times (Rs. 47,500 + Rs. 15,000) + \text{Development costs} = 15 \times Rs. 62,500 + Rs. 150,000 = Rs. 1,087,500[/tex]

  • Total profit or loss:

[tex]Rs. 1,050,000 - Rs. 1,087,500 = -Rs. 37,500[/tex] (a loss)

  1. For the car rental agency charges:

    Express the mileage charges [tex]C(x)[/tex] as a function of [tex]x[/tex]:

    • If [tex]0 \leq x \leq 100[/tex], then [tex]C(x) = 15x[/tex]

    • If [tex]x > 100[/tex], then [tex]C(x) = 15 \times 100 + 9(x - 100) = 1500 + 9(x - 100)[/tex]

    Calculate [tex]C(50)[/tex] and [tex]C(150)[/tex]:

    • [tex]C(50) = 15 \times 50 = Rs. 750[/tex]
    • [tex]C(150) = 1500 + 9 \times 50 = Rs. 1950[/tex]

  2. For the machine's depreciation:

    (i) The average yearly decrease in the value of the machine:

    [tex]\text{Average yearly decrease} = \frac{Rs. 4,000 - Rs. 400}{6} = Rs. 600[/tex]

    (ii) The equation for the value of the machine, [tex]V(t)[/tex], with age [tex]t[/tex] in years:

    [tex]V(t) = Rs. 4,000 - 600t[/tex]

    (iii) A schedule of the machine's value:

[tex]\begin{array}{|c|c|} \hline \text{Age in years (t)} & \text{Value of machine (Rs)} \\ \hline 0 & 4,000 \\ 1 & 3,400 \\ 2 & 2,800 \\ 3 & 2,200 \\ 4 & 1,600 \\ 5 & 1,000 \\ 6 & 400 \\ \hline \end{array}[/tex]

  1. For the firm's single product:

    (i) Construct the profit function [tex]P(x)[/tex]:

    [tex]P(x) = (\text{Selling price} - \text{Variable costs per unit}) \times x - \text{Fixed costs}[/tex]

    [tex]P(x) = (Rs. 65 - (Rs. 20 + Rs. 27.5)) \times x - Rs. 180,000[/tex]

    [tex]P(x) = Rs. 17.5x - Rs. 180,000[/tex]

    (ii) Calculate the profit for 20,000 units:

    [tex]P(20,000) = Rs. 17.5 \times 20,000 - Rs. 180,000 = Rs. 350,000 - Rs. 180,000 = Rs. 170,000[/tex]

  2. For the university football game:

    (i) To recover the Rs. 100,000 guarantee from ticket sales:

    [tex]0.25 \times 12 \times n = Rs. 100,000[/tex]

    [tex]3n = Rs. 100,000[/tex]

    [tex]n = \frac{Rs. 100,000}{3} \approx 33,333 \text{ tickets}[/tex]

    (ii) To achieve a net profit of Rs. 240,000:

    [tex]100,000 + 0.25 \times 12n = Rs. 240,000 + 100,000[/tex]

    [tex]0.25 \times 12n = Rs. 240,000[/tex]

    [tex]3n = Rs. 240,000[/tex]

    [tex]n = \frac{Rs. 240,000}{3} = 80,000 \text{ tickets}[/tex]

    (iii) If a sell-out of 50,000 fans is assured, find ticket price for desired profit of Rs. 240,000:

    [tex]100,000 + 0.25 \times 50,000 \times P = Rs. 240,000 + 100,000[/tex]

    [tex]0.25 \times 50,000 \times P = Rs. 240,000[/tex]

    [tex]12,500 \times P = Rs. 240,000[/tex]

    [tex]P = \frac{Rs. 240,000}{12,500} = Rs. 19.20[/tex]}

Thanks for taking the time to read 1 A firm is developing a TV advertising campaign Development costs fixed costs are Rs 150 000 and the firm must pay Rs 15 000. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada