Soni pruluces two types Of models A and B$.$t takes $1$ and $2$ manhours to produce rn$$lel A

ami B The company currently has $16$ employees who work $10$ hours Fr day on regular

and cm work another $2$ hours of overtime per day when Due to union regulations, these

workers cannot fired. The regular hourly pay is $10$ TL and overtime pay is $15\text{'}$ TL$.$ Each worker is

paid a minimum of IOx$10$zlW TL EM workday even ifhe is idle. ifnecessary, it is also possible to

hire temporary workers on a monthly basis at $20$ TLperhour. You can alsohire Frmanent workers at

a costofl$($m Assume$20$workdays

month and no significant hiring$/$firing costs for temporary workers. The inventory holding co$$t for

models can be approximated to be $3$ TL pa month pe$$ pr$$u$$jon hpwincurred.

infmmation for e$.$ach model for the next $4$ months is given below.

Month DemandforA DemandforB

$1$

$2$

$4$

$1500$

a$.(30$ pis$)$ Formulate an LP to minimize the total co$$t of production $($labor and inventory

holding$)$ for the next $4$ months. Ass$$me that all demand must be met on time.You must

define your variables clearly, write out the the constraints that must be satisfied

explaining the significance of each, and write the objective function with explanation.

b$.(5$ pts$)$ How would you modify this formulation if it is possible to backlog demand, but

there is a $50$ TL monthly co$$t per each backlogged unit?