Outline four aims of workstudy. Define motivation as a function of management. Highlight six factors to consider in determining the number of people in a span of control. State four benefits of delegation to each of the following in an organisation: supervisor; subordinates.

Muda uliozingatiwa (OT) kwenye jedwali ni nyakati za jumla. Tunahitaji kupata muda halisi kwa kila kipengele.

Mzunguko I:
$OT_{I,1} = 1.35 \text{ min}$
$OT_{I,2} = 2.65 - 1.35 = 1.30 \text{ min}$
$OT_{I,3} = 4.45 - 2.65 = 1.80 \text{ min}$
$OT_{I,4} = 6.75 - 4.45 = 2.30 \text{ min}$

Mzunguko II:
$OT_{II,1} = 12.65 - 6.75 = 5.90 \text{ min}$
$OT_{II,2} = 13.85 - 12.65 = 1.20 \text{ min}$
$OT_{II,3} = 15.48 - 13.85 = 1.63 \text{ min}$
$OT_{II,4} = 17.95 - 15.48 = 2.47 \text{ min}$

Mzunguko III:
$OT_{III,1} = 26.45 - 17.95 = 8.50 \text{ min}$
$OT_{III,2} = 27.95 - 26.45 = 1.50 \text{ min}$
$OT_{III,3} = 32.95 - 27.95 = 5.00 \text{ min}$
$OT_{III,4} = 34.60 - 32.95 = 1.65 \text{ min}$

$$AOT_1 = \frac{1.35 + 5.90 + 8.50}{3} = \frac{15.75}{3} = 5.25 \text{ min}$$ $$AOT_2 = \frac{1.30 + 1.20 + 1.50}{3} = \frac{4.00}{3} = 1.3333 \text{ min}$$ $$AOT_3 = \frac{1.80 + 1.63 + 5.00}{3} = \frac{8.43}{3} = 2.81 \text{ min}$$ $$AOT_4 = \frac{2.30 + 2.47 + 1.65}{3} = \frac{6.42}{3} = 2.14 \text{ min}$$

Tumia formula: $NT = AOT \times \frac{OR}{100}$

$$NT_1 = 5.25 \times \frac{95}{100} = 4.9875 \text{ min}$$ $$NT_2 = 1.3333 \times \frac{105}{100} = 1.4000 \text{ min}$$ $$NT_3 = 2.81 \times \frac{100}{100} = 2.8100 \text{ min}$$ $$NT_4 = 2.14 \times \frac{90}{100} = 1.9260 \text{ min}$$

$$TNT = NT_1 + NT_2 + NT_3 + NT_4$$ $$TNT = 4.9875 + 1.4000 + 2.8100 + 1.9260 = 11.1235 \text{ min}$$

$$RA_1 = 4.9875 \times \frac{25}{100} = 1.2469 \text{ min}$$ $$RA_2 = 1.4000 \times \frac{26}{100} = 0.3640 \text{ min}$$ $$RA_3 = 2.8100 \times \frac{32}{100} = 0.8992 \text{ min}$$ $$RA_4 = 1.9260 \times \frac{27}{100} = 0.5199 \text{ min}$$ $$TRA = 1.2469 + 0.3640 + 0.8992 + 0.5199 = 3.0399 \text{ min}$$

$$AT = TNT + TRA$$ $$AT = 11.1235 + 3.0399 = 14.1634 \text{ min}$$

Posho ya dharura ni 2%.

$$ST = AT \times \left(1 + \frac{\text{Posho ya Dharura}}{100}\right)$$ $$ST = 14.1634 \times \left(1 + \frac{2}{100}\right)$$ $$ST = 14.1634 \times 1.02$$ $$ST = 14.446668 \text{ min}$$

Kuzungusha hadi sehemu mbili za desimali:

$$ST \approx 14.45 \text{ min}$$

Muda wa kawaida kwa operesheni ni:

$$\boxed{\text{14.45 min}}$$