Q18: P.5.1) Please formulate the objective function.

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Q19: P.5.2) a) Please formulate the inventory balance constraints (Constraints (1)).

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Q20: P.5.2) b) Please formulate the ink usage constraints (Constraints (2): The provided ink must be used for

production)

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Q21: P.5.2) c) Please formulate the setup constraints (Constraints (3)).

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Q22: P.5.3) Can the presented problem become infeasible if the customer demand becomes very large? Please

explain!

Q23: P.5.4) a) Please adapt the objective function derived in exercise P.5.1).

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Q24: P.5.4) b) Please adapt the ink usage constraints (Constraints (2)) derived in exercise P.5.2 b).

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Time left 2:00:1 Question P.5 - Master production scheduling (17 Points) The writing utensils company ROBUSTO produces three different types of blue-colored pens (Rollerball, Felt- tip, Gel). Various information was gathered for the planning of production quantities for the upcoming weeks (see parameters). The production of each pen type requires a certain amount of ink. The company receives a fixed amount of ink each week due to long-lasting contracts with their supplier (the applying costs may be neglected). In case of large customer demands, additional ink may be purchased at a higher price. However, the ink cannot be stored and must be used for production For each pen type, the machines must be set up. Assume that setup costs but no setup times occur dependent on the type that is to be produced. Derive a linear algebraic planning model that minimizes the total costs! Use the following notation: Indices pe P:= {F,G, R} Set of pen types teT:= {1,...,E} Set of weeks Parameters dpt Demand for pens (in units) of type p in weekt Yp,o Inventory of pens (in units) of type p at the beginning of the planning horizon h Inventory holding costs per week and unit of pens of any type F Fixed amount of ink (in liters) received each week due to supplier contracts Ink (in liters) required to produce one unit of type p Additional purchasing costs per liter of ink ordered in addition to the fixed supply amount 8p Setup costs per setup process for pen type p M Big number Decision variables 2pt Production quantity of pens (in units) of type p in weekt Ypt Inventory of pens (in units) of type p at the end of weekt 7: Additionally ordered ink in liters) for production in weekt Zp,t is 1, if pen type p is set up in week to otherwise Yp,0 Inventory of pens (in units) of type p at the beginning of the planning horizon h Inventory holding costs per week and unit of pens of any type F Fixed amount of ink (in liters) received each week due to supplier contracts Time left 2:00:08 Ink (in liters) required to produce one unit of type p Additional purchasing costs per liter of ink ordered in addition to the fixed supply amount Sp Setup costs per setup process for pen type p M Big number Decision variables pt Production quantity of pens (in units) of type p in weekt Yp,t Inventory of pens (in units) of type p at the end of week t 72 Additionally ordered ink (in liters) for production in weekt Zpt is 1. if pen type p is set up in week t. 0 otherwise Please use the equation editor to type in your answers to the following questions! Use LaTex notation to type in your equation. To see how the equation is compiled based on your input, use the "equation editor" or "Formeleditor", which you can find in the drop-down of formatting options of the answer field. Also, the following LaTex commands can be helpful: Command Output x_{p.t} Ipt \sum _{p \in P} pep Neq \geq \forall V tlin T ter