Question

1. julia is planning to sell handmade candles at a craft fair. she wants to make at least $100 in profit, but also wants to ensure that she sells no more than 20 candles to maintain exclusivity. she decides to sell two types of candles: small candles, which she sells for $8 each, and large candles which she sells for $15 each. she estimates that she can make at most 15 large candles due to limited resources.

let x represent the number of small candles and y represent the number of large candles julia sells. what system of inequalities represents the profit constraint and constraint of candles sold?
a. 8x + 15y ≤ 100
x + y ≤ 20
y ≤ 15
b. 8x + 15y ≥ 100
x + y ≥ 20
y ≤ 15
c. 8x + 15y ≥ 100
x + y ≤ 20
y ≤ 15
d. 8x + 15y ≥ 20
x + y ≤ 100
y ≤ 15

Explanation:

Step1: Analyze the profit constraint

Julia wants to make at least $100$ in profit. The profit from small candles is $8x$ (since each small candle is $8$ dollars) and from large candles is $15y$ (since each large candle is $15$ dollars). So the profit inequality is $8x + 15y\geq100$ (at least means greater than or equal to).

Step2: Analyze the total number of candles sold constraint

She sells no more than 20 candles. The total number of candles is $x + y$, so the inequality is $x + y\leq20$ (no more than means less than or equal to).

Step3: Analyze the large - candle number constraint

She can make at most 15 large candles. So the inequality is $y\leq15$.

Answer:

C. \(8x + 15y\geq100\), \(x + y\leq20\), \(y\leq15\)