Hi - Helping a friend with the below but have no idea where to start
Any help / point in right direction appreaciated
A metal fabrication company produces bespoke metalwork with outstanding labour. They have an order for two types of metalwork, Metalwork 1 and Metalwork 2.
After delivering each unit of Metalwork 1, the company receives $3500 in profit, and each unit of the second metal work yields $5300 in profit. The production manager wants to investigate the number of units of each metalwork type to be produced during the next planning period.
The company only has 96000 labour hours available for the fabrication workshop next month. Fabricating a unit of Metalwork 1 requires 12 labour hours in the workshop, whereas a unit of Metalwork 2 requires 21 labour hours.
A recent closure of a key supplier of a special type of metal alloy led to a shortage of this alloy in the market. The company could secure only 20000KG of this alloy for the next month of production.
Production of Metalwork 1 and Metalwork 2 requires 4KG and 2KG of this alloy,respectively. Due to a decline in demand, the company does not manufacture more than 3500units of Metalwork 2. This means they do not expect a demand of more than 3500 units of Metalwork 2
.(a) Formulate a Linear Programming (LP) model for the presented problem that maximisesprofit. Use the graphical interpretation approach to solve the formulated model. Clearlypresent the LP model and the results of your developed model and solution.
(b) To restore Metalwork 2 demand to its previous state, the company attended andsponsored some manufacturing exhibitions in various market regions. The cost of suchactivities amounted to $480,000. The company expects that such marketing activitieswill raise the Metalwork 2 demand by 20%.Re-formulate the model presented in (a) considering the information described in (b) and present the new LP model.
Solve the developed model in (b) using the graphical interpretation approach. Conclude whether the company should participate in these marketing activities or not.
(c) Following some potential new hirings and equipment purchases, the production capacity could be increased by 25%. The production manager wants to investigate and check how this can affect the production of the two metal works. Modify the developed model in (a) accordingly, present the new model, solve it using the graphical interpretation procedures and present the results and solution step.
Any help / point in right direction appreaciated
A metal fabrication company produces bespoke metalwork with outstanding labour. They have an order for two types of metalwork, Metalwork 1 and Metalwork 2.
After delivering each unit of Metalwork 1, the company receives $3500 in profit, and each unit of the second metal work yields $5300 in profit. The production manager wants to investigate the number of units of each metalwork type to be produced during the next planning period.
The company only has 96000 labour hours available for the fabrication workshop next month. Fabricating a unit of Metalwork 1 requires 12 labour hours in the workshop, whereas a unit of Metalwork 2 requires 21 labour hours.
A recent closure of a key supplier of a special type of metal alloy led to a shortage of this alloy in the market. The company could secure only 20000KG of this alloy for the next month of production.
Production of Metalwork 1 and Metalwork 2 requires 4KG and 2KG of this alloy,respectively. Due to a decline in demand, the company does not manufacture more than 3500units of Metalwork 2. This means they do not expect a demand of more than 3500 units of Metalwork 2
.(a) Formulate a Linear Programming (LP) model for the presented problem that maximisesprofit. Use the graphical interpretation approach to solve the formulated model. Clearlypresent the LP model and the results of your developed model and solution.
(b) To restore Metalwork 2 demand to its previous state, the company attended andsponsored some manufacturing exhibitions in various market regions. The cost of suchactivities amounted to $480,000. The company expects that such marketing activitieswill raise the Metalwork 2 demand by 20%.Re-formulate the model presented in (a) considering the information described in (b) and present the new LP model.
Solve the developed model in (b) using the graphical interpretation approach. Conclude whether the company should participate in these marketing activities or not.
(c) Following some potential new hirings and equipment purchases, the production capacity could be increased by 25%. The production manager wants to investigate and check how this can affect the production of the two metal works. Modify the developed model in (a) accordingly, present the new model, solve it using the graphical interpretation procedures and present the results and solution step.
