X 23 x 33 10 hiring for day 3 x 32 x 42 x 23 x 33 10

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+ X 23 + X 33 £ 10 [Hiring for Day 3] X 32 + X 42 + X 23 + X 33 £ 10 [Hiring for Day 4] Objective (c) : To maximise cost while meeting demand of workers when temporary workers are hired by Alpha Steels due to an unexpected glut of orders. Additional Constraint Given : At least half of all money spent on workers goes to those who work 3 day shifts . ADDITIONAL CONSTRAINTS (d) Constraint of minimum money to be given to 3 day shift workers [250 x (X 12 + X 22 + X 32 + X 42 ) + 300 x (X 13 + X 23 + X 33 )] £ 300 x (X 13 + X 23 + X 33 ) 2 \ 300 x (X 13 + X 23 + X 33 ) - 250 x (X 12 + X 22 + X 32 + X 42 ) ³ 0
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Objective (d) : To maximise cost while meeting demand of workers when temporary workers are hired by Alpha Steels due to an unexpected glut of orders. Additional constraint given: There are 4 people willing to work a shift consisting of days 1, 2 and 5 for a payment of $110/day. ADDITIONAL CONSTRAINTS (e) Constraint of 4 people willing to work single shift on days 1, 2 and 5 @ $110/day Therefore, Number of Workers Hired Day 1 (Min 10 Workers) Day 2 (Min 15 Workers) Day 3 (Min 10 Workers) Day 4 (Min 15 Workers) Day 5 (Min 10 Workers) One Day Shift Workers X 11 X 21 - - X 51 Two Day Shift Workers X 12 X 22 X 32 X 42 - Three Day Shift Workers X 13 X 23 X 33 - - OBJECTIVE FUNCTION Therefore, the new objective of minimising hiring cost:- i.e minimise $110 x (X 11 + X 21 + X 51 ) + [One Day Shift Workers Total Pay] $250 x (X 12 + X 22 + X 32 + X 42 ) + [Two Day Shift Workers Total Pay] $300 x (X 13 + X 23 + X 33 ) + [Three Day Shift Workers Total Pay] (f) Minimum Workers Constraint For days 1, 3 & 5 at least 10 workers are needed:- X 11 + X 12 + X 13 ³ 10 [ Hiring for Day 1 ] X 22 + X 32 + X 13 + X 23 + X 33 ³ 10 [Hiring for Day 3] X 51 + X 42 + X 33 ³ 10 [ Hiring for Day 5 ] For days 2 & 4 at least 15 workers are needed:- X 21 + X 12 + X 22 + X 13 + X 23 ³ 15 [ Hiring for Day 2 ] X 32 + X 42 + X 23 + X 33 ³ 15 [Hiring for Day 4] (g) The number of one day shift workers (on day 1, 2 & 5) have to be £ 4 \ X ij £ 0 ; for i = 1, 2, 5 and j = 1 (h) Number of each category of workers ³ 0 \ X ij ³ 0 ; for i = 1, 2, 3, 4, 5 and j = 1, 2, 3
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