Question

A company produces popsicles, strawberry and cola flavor are processed using two different machines. Machine A can only be operated for 5 hours a day, while machine B can only be operated for 9 hours a day. The strawberry popsicles require one hour in machine A and three hours in machine B, while the cola popsicles require two hours in machine A and two hours in machine B. Profits from the strawberry popsicles and cola popsicles are RM5 and RM9, respectively. Use the Simplex Method to determine the maximum number of these products that needs to be produced daily for maximum profit (NOTE: the point of intersection must be shown correctly on a scaled graph paper and verified using solutions from simultaneous equations).

Answer 1

The Simplex Method can be used to find the maximum number of strawberry and cola popsicles that need to be produced daily for maximum profit. The problem involves constraints related to the operating hours of two machines and the production time of each popsicle flavor. The objective is to maximize profit.

Step-by-step explanation:

The Simplex Method can be used to determine the maximum number of strawberry and cola popsicles that need to be produced daily for maximum profit. Let's denote the number of strawberry popsicles as x and the number of cola popsicles as y.

The constraints for machine A and machine B can be written as:

• x + 2y ≤ 5 (Machine A constraint)
• 3x + 2y ≤ 9 (Machine B constraint)

The objective function for maximum profit can be written as:

• Profit = 5x + 9y

We can then solve this linear programming problem using the Simplex Method to find the maximum values of x and y that satisfy the constraints and maximize the profit.