Key constraints:

There's a one$-$week delay between your customer sending an order and you receiving it$.$ Similarly, there's a one$-$week delay between you sending an order to your supplier and them receiving it$.$

Inventory holding cost is $0\mathrm{.}5$ per unit per week, and backorder cost is $1$ per unit per week. Backorder implies that you can't fulfil the demand due to a lack of inventory but have promised to ship it as soon as you have stock. In turn, you pay a penalty $-$ in effect, it's not a 'lost sale' but a contractual penalty for delay.

Only your customer's demand is visible to you, and only your supplier can see your demand. Your 'customer' & 'supplier' would depend on your position in the supply chain.

The demand from the 'end customer' stays flat and jumps up$/$down at times. Unfortunately, you don't know what the future holds :$($

You aim to keep your cost in control and contribute to keeping the overall supply chain cost in control.