Given the following linear programming problem, maximize the solution and then explain how you arrived at your answer. Include the following:
In The Moment Café, a local eatery, Chef Marie has noticed that the ordering of supplies was not correct last month. This month, she wants to maximize her profit while ordering the correct amount of supplies. To maximize her profit, Marie needs to optimize the function f(x) = 10y – 0.5x
Because of the addition of a new office building nearby, her number of customers has doubled from 100 to 200; however, the amount of flour she needs to make her signature bread has only increased by a half, from 20 lbs. to 30 lbs. Another office building is due to open next month, and she needs to figure out how much flour to purchase given the current conditions.
The limitations of her current location are both in storage and number of customers to serve. Her facility can only hold 100 lbs. flour and serve 400 customers.
Variables: x = pounds of flour; y = number of customers
Constraints: 0 < x < 100; 0 < y < 400; y < 10x – 100
Function to maximize: f(x) = 10y – 0.5x