Nighttime Treats

Johnna Stewart

The business I have designed is a blanket and pillow shop. We have started with two products; blankets and pillows. The customers will be able to pick from a variety of fabrics in order to customize their own blankets and pillows.

Restrictions

I can only spend \$600 a month to make both blankets and pillows. Due to this, I can only make 24 blankets in a month and 20 pillows in a month. However, I must sell blankets and pillows every month. It will cost me \$25 to make a blanket and \$30 to make a pillow. Both pillows and blankets will sell for \$35 each. I can not spend more than \$450 on either project as I can not spend more than three quarters of my money on the production of one product.

Systems and Equations

X= number of blankets

Y= number of pillows

Profits and Costs

25x + 30y = Cost

35x + 35y = Sell

10x + 5y = Profit

Restrictions

25x + 30y ≤ 600

x ≤ 24

x > 0

25x ≤ 450

y ≤ 20

y > 0

30y ≤ 450

Maximizing Profit

Profit:

P= 10x + 5y

Feasible Vertices

(0,0); 10(0) + 5(0) =0

(18,4); 10(18) + 5(4) = 200

(5,15); 10(5) +5(15) = 125

(0,15); 10(0) + 5(15) = 75

(18,0); 10(18) + 5 (0) = 180

Conclusion

In order to maximize my profit I must make 18 blankets and 4 pillows per month for a total profit of \$200.