https://file.aiquickdraw.com/mathbot/file/1727288723263x7rpmb03.jpg

based on the report Is it beneficial to ask the workers to work overtime for additional 20 drilling hours at $20/hr?

Yes

No

The reports are not sufficient to tell

To determine whether it is beneficial to ask workers to work an additional 20 drilling hours at $20/hour, we need to assess the impact of the additional drilling hours on the system, particularly the production objective.

### Key data from the report:
- **Drilling Total Used** (constraint) has a **shadow price** of 45.917, meaning that for each additional unit (hour) of drilling time, the objective function (total revenue) would increase by 45.917 units of currency.
- **Current drilling hours** used are 90, and the **Allowable Increase** for the drilling constraint is 5.889 hours, which suggests that only an additional ~5.9 hours can directly contribute to improving the objective without violating the current constraint.
- **Cost of Overtime**: Additional drilling hours cost $20 per hour, so for 20 hours, the total cost would be $ 20 \times 20 = 400 $.

### Calculation:

1. **Maximum Benefit from Additional Drilling**:
   The shadow price indicates the revenue increase for each additional hour of drilling, but since only up to 5.889 hours are within the allowable range, we calculate:
   \[
   \text{Increase in revenue} = 5.889 \times 45.917 = 270.61
   \]
   This is the maximum possible revenue increase due to additional drilling hours within the allowable limit.

2. **Cost for 20 Hours**:
   The cost of 20 additional hours is:
   \[
   20 \times 20 = 400
   \]

3. **Comparison**:
   The benefit (270.61) is less than the cost (400). Therefore, it is **not beneficial** to pay for 20 additional hours of drilling at $20 per hour under these conditions.

### Conclusion:
**No**, it is not beneficial to ask the workers to work overtime for 20 drilling hours at $20/hour, as the cost outweighs the potential benefit.

---

Do you have any questions or need further clarification?

Here are 5 related questions:
1. How does the shadow price impact decision-making in linear programming?
2. Can increasing other resource constraints improve overall profitability?
3. What would happen if the overtime rate were lowered—would it change the conclusion?
4. How does the allowable increase in drilling hours influence the decision?
5. Could changes in production quantities (for parts) shift the cost-benefit balance?

**Tip**: Shadow price reflects the marginal benefit of relaxing a constraint, but it only applies within the allowable increase range. Beyond that, its effect may not hold.

Is it beneficial to ask the workers to work overtime for additional 20 drilling hours at $20/hr?

Explore whether it is cost-effective to ask workers for 20 extra drilling hours at $20 per hour, using linear programming's shadow price analysis. This problem involves understanding constraints and shadow prices.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation