3.1. Fixed ordering cost

The fixed ordering cost in the length of a finite horizon 0, t_1

3.1. Fixed ordering cost

The fixed ordering cost in the length of finite horizon 0, t_1

TC_A=A (5)

3.2. Purchasing cost

According to fig.1 of inventory level the purchasing cost of
?TC?_P=(CD(e^(??t?_1 )-e^((?t_1)/2)))/?-(?Q_1 t_1)/2 (6)

3.3. Holding cost excluding interest cost

We locate the average inventory quantity to obtain holding cost
?TC?_h=I_h ?_0^(t_1)??I(t)dt-I_(hQ_1 t_1 )/2=?_0^(t_1)??(D(e^(??t?_1 )-e^((?t_1)/2)))/?dt-I_(hQ_1 t_1 )/2=(I_h D)/?^2 (e^(?t_1 )-2e^((?t_1)/2)+1)-(???I?_h Q?_1 t_1)/2 ?? (7)

3.4. Optimal inventory level and optimal time

To obtain the EOQ by optimizing the total cost

TC=?TC?_A+?TC?_h+?TC?_P (8)

By subsisting Eq. (5, 6, 7) in Eq. (8)
Then
TC=A +(CD(e^(??t?_1 )-e^((?t_1)/2)))/?-(??Q?_1 t_1)/2+(I_h D)/?^2 (e^(?t_1 )-2e^((?t_1)/2)+1)-(??I_h Q?_1 t_1)/2 (9)

Deputy the t_1=(2Q_1)/(D-?Q_1 ) in Eq. (9)

TC=A +(CDQ_1/(D-??Q?_1 ))-C(?Q_1?^2/(D-??Q?_1 ))-(?I_h ?Q_1?^2)/((D-??Q?_1)) (10)

Deviating Eq. (10) with respect to Q_1

(d?TC?_1)/(dQ_1 )=CD(D/(D-??Q?_1 )^2 )-C( (2DQ_1-???Q?_1?^2)/(D-?Q_1 )^2 )-?I_h ((2DQ_1-???Q?_1?^2)/(D-??Q?_1 )^2 )=0

?Q_1?^*=D/? 1-(1-?C/(C+?I_h ))^(1/2)

Or
?Q_1?^*=D/? 1+(1-?C/(C+?I_h ))^(1/2)

Lemma (1):

a) If 0?k_1?1
i) ??D?Q?_1?^* If ?Q_1?^*=D/? 1-(1-?C/(C+?I_h ))^(1/2)

When k_1?? , 0?k_1?1
ii) ??D>Q?_1?^* If ?Q_1?^*=D/? 1-(1-?C/(C+?I_h ))^(1/2)

When k_1

3. Discuss at length how partnership working delivers better outcomes and what those outcomes are. Partnership working can deliver better outcomes when all parties are working together towards the same goals for the service user. parties have a good mutual knowledge about the individual they are delivering the service to and they are aware of each other’s input, they all have similar goals. In our work setting, outcome-based practice is to deliver our services which is measured by outcomes of support. From the initial assessment it is made clear what outcomes are expected or work towards. We will draw up a pen picture document the details of support that the individual requires and a summary of their character and required outcomes. The staff and individual will work together to plan for the individuals care/support and agree on what they want to see change in their life. The outcome will be what they will or have achieved with the work the staff and individual puts in. (1.3).

4. What barriers are there to partnership working and how can you overcome those barriers? Common barriers that can be found with working partnerships could include lack of communication or poor communication. Incorrect record keeping, misunderstanding of situations, or not following policies or procedures. The lack of communication can cause problems if for instance the carers work in double (pairs) and they have a disagreement with each other, then they may not have as effective communication as they would normally have because one being upset etc this could affect the way the care would be delivered to the service user, this could also have an effect on the service user emotionally. The misunderstanding could be due to language barrier to what they say or the way they say it or pronounce requests the wrong way. Information that you pass on must always ensure what is a clean indication of the situation and that it has been received clearly. so we need to ensure we listen to the people were communicating with. If the documentation is incorrect this could cause a problem and may result in incorrect needs being achieved, lack of information being passed from one agency to another, so we need to ensure that the correct information is passed on from one agency to another. Avoid using jargon i.e UTI as I have been in care work for a length of time I have knowledge of certain abbreviations ,but to new carers this jargon may mean nothing to them. When working in partnership we work with people from different cultures, races and religions ,what I might interpret as normal, people from different cultures may consider odd or may offensive. In a multicultural environment problems
One terrible situation was when agency’s working with a child had failed to pass on or the lack of information being passed on from one agency to another, this had contributed to the death of Victoria Climbie (2000).