The price of a packet of milk is (50 + 4n) shillings and the number of packets sold is (530 − 20n). Find the…

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The price of a packet of milk is (50 + 4n) shillings and the number of packets sold is (530 − 20n). Find the total sales in simplified expanded form and the number of times the price was increased to

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Here are the solutions for the next parts: a) iii) The total sales in simplified expanded form after the price of packet of milk was increased: Step 1: Recall the expressions for the price and the number of packets sold. From previous parts: Price per packet = (50 + 4n) shillings; Number of packets sold = (530 − 20n) packets Step 2: Formulate the expression for total sales. Total sales are calculated by multiplying the price per packet by the number of packets sold. Total Sales = (50 + 4n)(530 − 20n) Step 3: Expand the expression by multiplying the terms. Total Sales = 50(530) + 50(−20n) + 4n(530) + 4n(−20n); Total Sales = 26500 − 1000n + 2120n − 80n² Step 4: Combine like terms and write the expression in simplified expanded form (standard quadratic form). Total Sales = −80n² + (2120 − 1000)n + 26500; Total Sales = −80n² + 1120n + 26500 The total sales in simplified expanded form are −80n² + 1120n + 26500. b) Determine: i) The number of times the price was increased to attain maximum sales: Step 1: Use the total sales expression from part (a-iii). The total sales function is a quadratic equation: S(n) = −80n² + 1120n + 26500. This is in the form an² + bn + c, where a = −80, b = 1120, and c = 26500. Since a is negative, the parabola opens downwards, meaning it has a maximum point. Step 2: Calculate the value of n at which the maximum sales occur. The n-coordinate of the vertex of a parabola is given by the formula n = (−b)/(2a). n = (−1120)/(2(−80)); n = (−1120)/(−160) Step 3: Simplify the value of n. n = 112/16; n = 7 The number of times the price was increased to attain maximum sales is 7 times.

The price of a packet of milk is (50 + 4n) shillings and the number of packets sold is (530 - 20n). Find the total sales in simplified expanded form and the number of times the price was increased to

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Step-by-step solution

Part a(iii)· 4 steps

Recall the expressions for the price and the number of packets sold.

Formulate the expression for total sales.

Expand the expression by multiplying the terms.

Combine like terms and write the expression in simplified expanded form (standard quadratic form).

Part b(i)· 3 steps
$7 \text{ times}$

Use the total sales expression from part (a-iii).

Calculate the value of $n$ at which the maximum sales occur.

Simplify the value of $n$ .

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