Question

A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 3 hours of fabrication and 1 hour of assembly, and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to 950 labor-hours of fabrication time and 700 labor-hours of assembly time available per week. The profit on each component, A, B, and C, is $7, $8, and $10, respectively. How many components of each type should the company manufacture each week in order to maximize its profit (assuming that all components manufactured can be sold)? What is the maximum profit? Let xt,X2, and x be the numbers of components A, B, and C, respectively, that get manufactured. Construct a mathematical model in the form of a linear programming problem Maximize p subject to Fabrication Sme restriction Assembly time restriction he te 1220 Suppose that a furniture manufacturer makes chairs, sofas, and tables. Consider the following chart of labor hours required and available. Carpentry 63 Chair Sofa Table Daily labor available (labor-hours) Finishing Upholstery2 720 140 244 6 The profit per chair is $100, per sofa $70, and per table $140. How many pieces of each type of furniture should be manufactured each day to maximize the profit? chairs, sofas, and tables should be manufactured each day to maximize the profit

Answer 1

Let us assume that Number of components A's that should be maufactured. 2 Number of components B's that should be manufactured. 3 Number of components C's that should be manufactured. subject to: 2r1 3r2 + 2r3 < 950 i+2+2r3 s 700 11, r2, r30

2 Let us assume that Nmber of chairs that should be mamifactured. 2 Number of sofas that should be manufactured. r3 = Number of tables that should be manufactured. max:- 1001 70r2 +140r3 subject to: 6x1 +3r2+8r3 s 720 ri +r2+2rs 140 2r1 6r2+0r3 244 r1, 2, r320

14 0 3 Si o 어a 244 23 2 x31140 3ㅇ o O 7 x31H02 = 12 380