Set up (but do not attempt to solve) the linear programming problem (i.e. give t

Question

Set up (but do not attempt to solve) the linear programming problem (i.e. give the objective function, state whether it is to be maximized or minimized, and list all constraints). A cabinet shop makes and sells two types of cabinets, type 1 for the kitchen and type 2 for the bathroom. Manufacture of the cabinets consists of two steps, making the frames and drawers and then assembling and finishing the units. Labor requirements, in hr/unit, are as follows: Each week the shop has 480 hr of labor available for the manufacture of the cabinets. However, to conserve labor, frames and drawers completed and ready for assembly and finishing can also be bought from a local dealer at a cost of $200 for a kitchen frame/drawer set and $110 for a bathroom frame/drawer set. THe kitchen cabinets sell for $350 each: the first 70 bathroom cabinets sell for $250 per unit, but any more produced sell for only $225 per unit. We assume that all units produced will be sold. Use the following variables: t_i = the total number of cabinets of type i produced, i = 1,2 m_i = the number of frames/drawers made of type i b_i = the number of frames/drawers bought of type i u = the number of bathroom cabinets sold up to 70 v = the number of bathroom cabinets sold over 70

Explanation / Answer

maximize

Z = 350 t1 + 250 u + 225 *( v ) - 200 b1 - 110 b2

(2.6 + 2.1) m1 + (1.5 +1.8 ) m2 + 2.1 b1 + 1.8 b2 < 480   {labour constraint}

m1 + b1 = t1    {total in kitchen}

m2 + b2 = u + v    {total in bathroom}

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