A leather goods factory manufactures five styles of handbags, whose variable contributions are £30, £40, £45, £25, £60 per dozen respectively. The products must pass through four work centres and the person-hours available in each are: clicking (700), paring (600), stitching (400) and finishing (900). Hourly requirements for each dozen handbags are:
Style Click Pare Stitch Finish
341 3 8 2 6
262 4 3 1 0
43 2 2 0 2
784 2 1 3 4
5-A 5 4 4 3
To prevent adding to inventory levels already on hand, the Production Manager, after reviewing the weekly sales forecasts, has specified that no more than 100, 50, 90, 70, and 30 dozen of each style respectively may be produced. Each handbag is made from five materials as specified in the following table:
units of materials per dozen
Style Leather Fabric Backing Lining Accessories
341 0 1 4 2 3
262 4 0 7 4 4
43 5 7 6 2 0
784 6 4 1 1 2
5-A 2 3 3 0 4
Total Units
Available 300 400 1,000 900 1,600
Question
{ Formulate a linear program for next week's optimum manufacturing schedule if overall contribution is to be maximised.
NOTE: define variables first, then objective function, and then constraints!