Question

Jordan and Payton are friends with the owners of a pet sitting business and are thinking that starting a business to make money in the summer is a good idea. They are thinking that they will sell emergency items. Start-up costs: Jordan and Payton can spend up to $45 that they have saved to start their business. They are planning to sell flashlights and emergency blankets. They have a supplier that they can purchase these items from. Their cost will be $3 per blanket and $5 per flashlight. Income Requirements: Jordan and Payton are planning to sell the blankets for $6 each and sell the flashlights for $10 each. Their parents have told them that if they are not able to make more than $180, then they need to do something else, so they have made it a goal to make more than $180. Use Desmos to graph the system of equations. Then make a recommendation to Jordan and Payton about where or not this will be a good business venture.

Answer 1

Analyzing the graph, if there's a positive integer solution within the feasible region, it indicates that Jordan and Payton can meet their cost and income goals. If there's no solution or only fractional solutions, they might need to reconsider their pricing or explore alternative business ideas.

Since there's no solution or only fractional solutions, they might need to reconsider their pricing or explore alternative business ideas.

Let x be the number of blankets and

y be the number of flashlights. The system of equations representing the cost and income is:

Cost Equation:

3x+5y≤45 (Total cost not exceeding their savings)

Income Equation:

6x+10y>180 (Goal of making more than $180)

The region where the shaded area of the two inequalities overlap is the feasible solution.

For the cost equation:

3x+5y≤45

For the income equation:

6x+10y>180

The shaded region where these two overlap is the solution space that satisfies both conditions. If this region allows for positive integer solutions for x and y (since you can't sell a fraction of a blanket or flashlight), then it's a feasible business venture.