The Adventure Pty Ltd, an equipment and clothing manufacturer, decided to begin production of two new unisex parkas designed for use in extremely cold weather conditions. The names selected for two models are Mount Everest Parka and Denali Parka. Their manufacturing plant has 140 hours of cutting time and 100 hours of sewing time available for producing these two parkas in large size. Each Mount Everest Parka in large size requires 45 minutes of cutting time and 60 minutes of sewing time. Each Denali parka in large size requires 35 minutes of cutting time and 30 minutes of sewing time. The labour and material cost is $180 for each Mount Everest parka and $90 for Denali parka. The retail prices through the company's online store are $450 for Mount Everest parka and $300 for Denali parka. The company's management has specified that at least 25% of the total production of new parkas must consist of Mount Everest parka. Assume that the Adventure Pty Ltd can sell as many large size coats as they can produce.
Formulate the linear programming problem to maximise the profit made by the company.
The LP formulation must include the definition of decision variables and the linear program consisting of the objective function and constraints.