# Betwixt

### Our Mission

My business Betwixt will be a luxury bath business that focuses on making your bath feel like a spa day. The two main products we will be selling will be bath bombs, and candles. Made with all natural ingredients and no unnatural dyes or perfumes are products are safe for even the most sensitive skin. The bath bombs are sold individually wrapped and the candles are sold in 14.50z jars with 3-wicks.

# Bath Bombs

Our bath bombs at Betwixt will come in 2 shapes. The main shape will be a sphere, followed by a square and seasonal bath bombs will come in many different shapes. The bath bombs will cost \$1.00 to make and I will sell them for \$3.25. I will not be able to make more than 250 bath bombs each month, and I cannot spend more than \$7500 total on the bath bombs. Each month I cannot spend more than \$950.00 on each product.

# Candles

The candles will come in 14.5oz jars. Each 3-wick candle only cost \$3.00 dollars to make and I will sell them for \$10.00 each. The 3 different types of candles are Flannel, Lemon Mint Leaf and Vanilla Chai. I cannot make more than 125 candles each month and I cannot spend more than \$7500 on this one product. Each month I cannot spend more than \$950.00 on each product.

# Restriction Inequalities.

### x = Bath Bombs and y = Candles

• X ≥ 0, X ≤ 250
• Y ≥ 0, Y ≤ 125
• X + 2y ≤ 950
• 1x ≤ 7500, 3y ≤ 7500

# Profits

### The amount of money earned subtracted by the cost to make the products

Cost: 1x+3y

Earned: 3.25x+ 10y

Profit = (3.25x + 10y) – (1x + 3y)

# Maximizing Profits

(0,125) P=3.25(0) + 10(125) – 1(0) + 3(125)=\$875

(0,0) P=3.25(0) + 10(0) - 1(0) +3(0)=\$0

(250,0) P=3.25(250) + 10(0) - 1(250) + 3(0)=\$562.50

250,125) P= 3.25(250) + 10(125) -1(250) + 3(125)=\$1437.50

To maximize my profits I will need to make 250 bath bombs and 125 candles each month.