Final answer:
After 3 hours, Closet Wizards and their competitors will charge the same amount which is $105. It's more economical for a consultant who earns $200 per hour to buy vegetables because the opportunity cost of gardening is higher than the cost of purchasing them.
Step-by-step explanation:
To determine after how many hours Closet Wizards and their competitors charge the same amount, we set up an equation where both companies' cost functions are equal to each other. This can be represented as:
Closet Wizards: $45 + $20 × hours
Competitor: $30 + $25 × hours
We find the number of hours at which the total cost is the same for both by solving the equation:
45 + 20 × hours = 30 + 25 × hours
This simplifies to:
5 × hours = 15
hours = 3
So, after 3 hours, both companies will charge the same amount. To calculate the charge, we just insert the number of hours back into either company's cost function:
Closet Wizards: $45 + $20 × 3 = $105
Competitor: $30 + $25 × 3 = $105
Both companies will charge $105 after 3 hours of work.
Regarding the consultant who earns $200 per hour, it makes more economic sense for her to continue her consulting job rather than grow her own vegetables. The opportunity cost of her spending time gardening instead of consulting is the lost wages she could have earned during that time. Therefore, purchasing vegetables is more economical given her high hourly earning potential.