This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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 - 80n^2 Step 4: Combine like terms and write the expression in simplified expanded form (standard quadratic form). Total Sales = -80n^2 + (2120 - 1000)n + 26500 Total Sales = -80n^2 + 1120n + 26500 The total sales in simplified expanded form are -80n^2 + 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) = -80n^2 + 1120n + 26500. This is in the form an^2 + 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. Last free one today — make it count tomorrow, or type /upgrade for unlimited.