NEED EXCEL SOLVER!!!!!

National Wing Company (NWC) is gearing up for the new B-48 contract. NWC has agreed to produce 20 wings in April, 24 in May, and 30 in June. Currently, NWC has 100 fully qualified workers. A fully qualified worker can either be placed in production or can train new recruits. A new recruit can be trained to be an apprentice in one month. After another month, the apprentice becomes a qualified worker. Each trainer can train two recruits.

The production rate and salary per employee type is listed below.

Type of Employee	Production Rate (wings/month)	Wage per month
Production	0.6	$3,000
Trainer	0.3	$3,300
Apprentice	0.4	$2,600
Recruit	0.05	$2,200

At the end of June, NWC wishes to have no recruits or apprentices, but have at least 140 full-time workers.

Considering the above limitations, write a linear programming model to help NWC determine the number of employees in each type at each month (April, May, June) so as to minimize total wedge cost.

1.Define the Decision Variables

Pi = number of producers in month i (where i = 1, 2, 3 for April, May, June)

Ti = number of trainers in month i (where i = 1, 2 for April, May)

Ai = number of apprentices in month i (where i = 2, 3 for May, June)

Ri = number of recruits in month i (where i = 1, 2 for April, May)

2.Define the Objective Function

Minimize total wage cost for producers, trainers, apprentices, and recruits for April, May, and June: Min 3000P1 + 3300T1 + 2200R1 + 3000P2 + 3300T2 + 2600A2+2200R2 + 3000P3 + 2600A3

3.Define the Constraints

Total production in Month 1 (April) must equal or exceed contract for Month 1: (1) .6P1 + .3T1 +.05R1 > 20

Total production in Months 1-2 (April, May) must equal or exceed total contracts for Months 1-2: (2) .6P1 + .3T1 + .05R1 + .6P2 + .3T2 + .4A2 + .05R2 > 44

Total production in Months 1-3 (April, May, June) must equal or exceed total contracts for Months 1-3: (3) .6P1+.3T1+.05R1+.6P2+.3T2+.4A2+.05R2+.6P3+.4A3 > 74

In April there are 100 employees that can be producers or trainers: (4) P1 + T1 = 100

At the end of June, there are to be at least 140 employees: (5) P3 + A3 > 140

Each trainer can train two recruits: (6) 2T1 > R1

(7) 2T2 > R2

The number of producers and trainers in a month must equal the number of producers, trainers, and apprentices in the previous month

(8) P1 + T1 = P2 + T2

(9) P2 + T2 + A2 = P3

The number of apprentices in a month must equal the number of recruits in the previous month:

(10) A2 = R1

(11) A3 = R2

Non-negativity: P1, T1, R1, P2, T2, A2, R2, P3, A3 > 0