Answer:
c) 4 simple vases and 4 elaborate vases maximize profit.
The maximum profit is $260.
Explanation:
Given information:
- A glass blower can form 8 simple vases or 2 elaborate vases in an hour.
- In a work shift of no more than 8 hours, the worker must form at least 40 vases.
Part (a)
Define the variables:
- Let s = the number of hours forming simple vases.
- Let e = the number of hours forming elaborate vases.
Create a system of inequalities using the given information and defined variables:
Part (b)
Given information:
- $30 = profit per hour for the simple vases.
- $35 = profit per hour for the elaborate vases.
Let y be the total profit in dollars:
Part (c)
To find the number of hours the worker should spend on each type of vase to maximize profit, find the point of intersection of the two equations.
Isolate e in the first equation:
Isolate e in the second equation:
Equate the two expressions for e and solve for s:
Therefore, the number of hours the worker should spend on each type of vase to maximize profit is:
- Simple vases = 4 hours.
- Elaborate vases = 4 hours.
Substitute the values of s and e into the function from part (b):
Therefore, the maximum profit is $260.