The owner of a machine shop is planning to expand by purchasing some new machines—presses and lathes. The owner has estimated that each press purchased will increase profit by ₱5000 per day and each lathe will increase profit by ₱7500 daily. The number of machines the owner can purchase is limited by the cost of the machines and the available floor space in the shop. The machine purchase prices and space requirements are as follows: Required Floor Space (m2) Purchase Price Press 1.4 ₱400,000 Lathe 2.8 200,000 The owner has a budget of ₱2,200,000 for purchasing machines and 22 square meters of available floor space. a. Formulate an integer programming model to determine how many of each type of machine to purchase to maximize the daily increase in profit. b. Solve the model formulated in part (a) without integer requirements. What are the optimal solution for the press and the lathe machines? What is the optimal profit? c. Round the press and lathe values found in part (b). Is the solution feasible? Why? d. Truncate the press and lathe values found in part (b) (i.e drop the fractional part of each value). Is the solution feasible? Why? e. Add integer requirements to the model you constructed in part (b). What is the optimal profit and what are the optimal number of press and lathe machines?
The owner of a machine shop is planning to expand by purchasing some new machines—presses and lathes. The owner has estimated that each press purchased will increase profit by ₱5000 per day and each lathe will increase profit by ₱7500 daily. The number of machines the owner can purchase is limited by the cost of the machines and the available floor space in the shop. The machine purchase prices and space requirements are as follows:
| Required Floor Space (m2) | Purchase Price | |
| Press | 1.4 | ₱400,000 |
| Lathe | 2.8 | 200,000 |
The owner has a budget of ₱2,200,000 for purchasing machines and 22 square meters of available floor space.
a. Formulate an integer programming model to determine how many of each type of machine to purchase to maximize the daily increase in profit.
b. Solve the model formulated in part (a) without integer requirements. What are the optimal solution for the press and the lathe machines? What is the optimal profit?
c. Round the press and lathe values found in part (b). Is the solution feasible? Why?
d. Truncate the press and lathe values found in part (b) (i.e drop the fractional part of each value). Is the solution feasible? Why?
e. Add integer requirements to the model you constructed in part (b). What is the optimal profit and what are the optimal number of press and lathe machines?
Answer D and E
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