Operations Management$1$

#### Q$1)$CALCULATION BASED

A company produces widgets and has fixed costs of $$10,000$ per month. The variable cost per widget is $$2,$ and each widget sells for $$5.$

a$)$ Calculate the break$-$even point in units.

b$)$ How many units must be sold to achieve a monthly profit of $$6,000?$

#### Q$2)$ DIAGRAM MAKING

Draw and label a diagram of the Product Life Cycle $($PLC$).$ In your diagram, include and explain the four stages: Introduction, Growth, Maturity, and Decline.

#### Q$3)$ SUPPLY CHAIN

Consider a supply chain that involves a manufacturer, a distributor, and a retailer. The manufacturer produces a product that is then shipped to the distributor, who then ships it to the retailer.

a$)$ Describe the key functions and responsibilities of each entity in the supply chain.

b$)$ Discuss the potential challenges that can arise at each stage of the supply chain and suggest possible solutions to mitigate these challenges.

#### Q$4)$ FLOWCHART

Create a flowchart that outlines the process of order fulfillment in an e$-$commerce company, from the moment a customer places an order to the delivery of the product. Include the following steps:

$1.$ Order received

$2.$ Payment processed

$3.$ Order packed

$4.$ Order shipped

$5.$ Order delivered

#### Q$5)$ MATHS

A factory produces two types of products, A and B$.$ The production cost per unit of product A is $$10,$ and for product B$,$ it is $$15.$ The factory has a daily budget of $$1,200$ and can produce a maximum of $100$ units of product A and $80$ units of product B per day. The profit per unit of product A is $$6,$ and for product B$,$ it is $$8.$

a$)$ Formulate a linear programming model to maximize the daily profit.

b$)$ Solve the linear programming model to determine the optimal number of units of product A and product B to produce daily.