Substitute numerical values into linear and simple non-linear algebraic expressions, and evaluate.

A manufacturer calculates the production cost (in dollars) using the formula C = 15a + 0.8a² − 120, where a is the number of units produced. Calculate the production cost when 50 units are produced.

A retail business calculates the profit from selling a new product using the formula \(P = 45n - 1200 - 8n^2\), where \(P\) is the profit in dollars and \(n\) is the number of items sold. (a) Calculate the profit when \(n = 15\). [1 mark] (b) Calculate the profit when \(n = 25\). [1 mark] (c) State which production level (15 or 25 items) gives the greater profit. [1 mark]

A small manufacturing company produces and sells hand-crafted candles. The weekly profit (in dollars) is modelled by the expression $P = 18s - 250$, where $s$ is the number of candles sold. (a) Calculate the weekly profit when 45 candles are sold. (1 mark) (b) The production cost per candle is $\$4.50$. If the revenue function is $R = 22s$, determine the weekly profit using the expression $P = R - C$, where $C$ is the total cost, when 60 candles are sold. (2 marks)

A solar panel installation company uses the formula \(C = 450n + 3200 + \frac{8000}{n}\) to calculate the total cost \(C\) (in dollars) of installing \(n\) panels, where \(n \geq 5\). (a) Calculate the total cost for installing \(n = 10\) panels. (b) The company offers a payment plan where a client pays \(\frac{1}{4}\) of the total cost as a deposit, and the remaining balance in \(12\) equal monthly instalments. Calculate the monthly instalment amount for a client who chooses to install \(n = 16\) panels. Express your answer to the nearest dollar.