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Douglas McGregor's Theory X and Theory Y (1960):
| Theory X | Theory Y |
|---|---|
| Employees are inherently lazy | Employees are self-motivated |
| Dislike work and avoid it | Find work natural and satisfying |
| Need close supervision and control | Can be self-directed and creative |
| Motivate through punishment/rewards | Motivate through autonomy and responsibility |
In nursing management, Theory X leads to authoritarian leadership, while Theory Y encourages participative management. Most modern nursing management advocates Theory Y to improve staff engagement and retention.
If $\displaystyle\sum_{i=1}^{20} \left(\frac{{}^{20}C_{i-1}}{{}^{20}C_i + {}^{20}C_{i-1}}\right)^3 = \frac{k}{21}$, find $k$.
Use the identity: $\dfrac{{}^{20}C_{i-1}}{{}^{20}C_i + {}^{20}C_{i-1}} = \dfrac{{}^{20}C_{i-1}}{{}^{21}C_i} = \dfrac{i}{21}$
So the sum becomes: $\displaystyle\sum_{i=1}^{20}\left(\frac{i}{21}\right)^3 = \frac{1}{21^3}\sum_{i=1}^{20}i^3 = \frac{1}{21^3}\cdot\left(\frac{20\cdot21}{2}\right)^2 = \frac{(210)^2}{21^3} = \frac{44100}{9261} = \frac{200}{21}$
Therefore $k = \mathbf{200}$.
Budgeted data for 6,000 units:
- Variable manufacturing: $90,000
- Variable selling: $6,000
- Fixed manufacturing: $54,000
- Fixed admin: $21,000
Selling price is $40 unit. How many units must be sold to reach a target profit of $45,000?
1. Variable Cost per unit = ($90,000 + $6,000) / 6,000 = $16.
2. Contribution per unit = $40 - $16 = $24.
3. Total Fixed Costs = $54,000 + $21,000 = $75,000.
4. Required Units = (Fixed Costs + Target Profit) / Contribution = ($75,000 + $45,000) / $24 = 5,000 units.
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