You manage the supply chain of NovaTech, a leading tech company in the smart device industry.

Your task is to optimize the inventory of five critical components: Microchips, Batteries, Displays,

Sensors, and Casings. These components have varying costs, storage capacities, and are crucial for

daily production activities. The challenge is to purchase and manage these supplies over three days

to ensure production needs are met without exceeding storage capacities or depleting inventory

below critical levels, all while minimizing purchasing costs. The cost of each component and its

daily usage requirement $($demand$)$ will vary over the three$-$day period. The company incurs

inventory costs at the end of each day. This variation reflects market dynamics, such as supply

chain disruptions, demand surges, or discounts from suppliers.

Day $1$:

Component Cost per unit Demand

Microchips $$15\mathrm{.}0060$ units

Batteries $$5\mathrm{.}00110$ units

Displays $$20\mathrm{.}0040$ units

Sensors $$2\mathrm{.}50160$ units

Casings $$8\mathrm{.}0075$ units

Day $2$:

Component Cost per unit Demand

Microchips $$14\mathrm{.}5050$ units

Batteries $$4\mathrm{.}75100$ units

Displays $$19\mathrm{.}0030$ units

Sensors $$2\mathrm{.}75150$ units

Casings $$7\mathrm{.}5070$ units

ADM$2302$ Winter $2024$ Assignment $1$

Winter $2024$ Page $4$

Day $3$:

Component Cost per unit Demand

Microchips $$15\mathrm{.}5070$ units

Batteries $$5\mathrm{.}25120$ units

Displays $$21\mathrm{.}0035$ units

Sensors $$2\mathrm{.}25170$ units

Casings $$8\mathrm{.}5080$ units

Inventory and holding host information:

Component Holding Cost $($per unit$)$ Initial Inventory Maximum Capacity

Microchips $$0\mathrm{.}40100$ units $350$ units

Batteries $$0\mathrm{.}10100$ units $300$ units

Displays $$1\mathrm{.}0080$ units $300$ units

Sensors $$0\mathrm{.}50200$ units $600$ units

Casings $$0\mathrm{.}25120$ units $300$ units

Requirements

$1.$ Meet Daily Production Requirements: Ensure that the inventory is sufficient to meet the

variable daily demand for each component.

$2.$ Inventory Management:

$$ Initial Inventory Levels are given.

$$ Purchases add to the inventory based on variable daily prices.

$$ Usage depletes the inventory according to the variable daily demand.

$$ Inventory levels must stay within maximum capacity limits and above minimum

safety stock levels $($if applicable$).$

$$ The company incurs inventory costs at the end of each day.

$3.$ Purchasing requirements:

$$ Maximum of $100$ units of Microchips can be purchased on each day.

$$ Maximum of $200$ units of Batteries can be purchased on each day.

$$ Maximum of $50$ units of Displays can be purchased on each day.

$$ Maximum of $250$ units of Sensors can be purchased on each day.

$$ Maximum of $150$ units of Casings can be purchased on each day.

Formulate algebraically the above problem. Define the decision variables, objective function, and constraints.