AutoIgnite produces electronic ignition systems for automobiles at a plant in Cl

Question

AutoIgnite produces electronic ignition systems for automobiles at a plant in Cleveland, Ohio. Each Ignition system is assembled from two components produced at AutoIgnite's plants in Buffalo, New York, and Dayton Ohio. The Buffalo plant can produce 2000 units of component 1, 1000 units of component 2, or any combination of the two components each day. For instance, 60% of Buffalo's production time could be used to produce component 1 and 40% of Buffalo's production time could be used to produce component 2; in this case, the Buffalo plant would be able to produce 0.6(2000)=1200 units of component 1 each day and 0.4(1000)=400 units of component 2 each day. The Dayton plant can produce 600 units of component 1, 1400 units of component 2, or any combination of the two components each day. At the end of each day, the component production at Buffalo and Dayton is sent to Cleveland for assembly of the ignition system on the following workday.

a. Formulate a linear programming model that can be used to develop a daily production schedule for the Buffalo and Dayton plants that will maximize daily production of ignition systems at Cleveland.

b. Find the optimal solution

Explanation / Answer

a) Linear program is following:

Let B be the proportion of Buffalo's time used to produce component 1

D be the proportion of Dayton's time used to produce component 1

Daily production of component 1 = 2000B + 600D

Daily production of component 2 = 1000(1-B) + 1400(1-D) = 2400 - 1000B - 1400D

Production of component 1 must be equal to component 2 for assembly of ignition system.

Max 2000B+600D

s.t.

2000B + 600D = 2400 - 1000B - 1400D or,

3000B + 2000D = 2400

B <= 1

D <= 1

B, D >= 0

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.