A beverage can manufacturer makes three sizes of soft drinkcans—Small, Medium and Large. Production is limited by machineavailability, with a combined maximum of 105 production hours perday, and the daily supply of metal, no more than 200 kg per day.The following table provides the details of the input needed tomanufacture one batch of 100 cans for each size.
​
                                                                               Cans |
| Large | Medium | Small | Maximum |
| Metal (kg)/batch | 9 | 6 | 5 | 200 |
| Machines’ Time (hr)/batch | 4.4 | 4.2 | 4 | 105 |
| Profit/batch | $51 | $40 | $42 | |
​
a. Develop a linear programming model by identifying thevariables, writing the objective function
b. Write all necessary constraints
c. Find the maximized profit and determine how many batches ofeach can size should be produced.
