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# Linear Programming : Optimal Solution Using Graphical Methods

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The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and frilling. Each air conditioner takes 3 hours or wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of \$25.00. Each fan assembled may be sold for a \$15.00 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach.

Electrocomp's management realized that it forgot to include two critical constraints (see Problem above). In particular, management decides that to ensure an adequate supply of air conditioners for a contract, at least 20 air conditioners should be manufactured. Because Electrocomp incurred an over supply of fans in the preceding period, management also insists that no more than 80 fans be produced during this production period. Resolve this product mix problem to find the new optimal solution.

##### Solution Summary

The optimal solution to a linear programming problem is found using graphical methods. The solution is detailed and well presented. Attached as a 3-paged Word document with displayed calculations and a graph to aid understanding.

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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