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
You're on a roll — 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. What's next? Send 'em!