TCO 2 Bieber Company has excess capacity on two machines 24

(TCO 2) Bieber Company has excess capacity on two machines, 24 hours on Machine 105 and 16 hours on Machine 107. To use this excess capacity, the company has two products, known as Product D and Product F, that must use both machines in manufacturing. Both have excess product demand, and the company can sell as many units as it can manufacture. The company’s objective is to maximize profits.
Product D has an incremental profit of $6 per unit, and each unit utilizes 2 hours of time on Machine 105 and then 2 hours of time on Machine 107. Product F has an incremental profit of $7 per unit, and each unit utilizes 3 hours of time on Machine 105 and then 1 hour of time on machine 107. Let D be the number of units for Product D, F be the number of units for product F, and P be the company’s profit.
The equations 2D + 3F < 24, D > 0, and F > 0 are

Solution

Objective Function : Maximise P where P=6D + 7F

Constraints of machine hours

2D + 3F < 24 ,

2D + F <16

where D >0, F > 0

where D and F are the number of units of Product D and Product F respectively.