Question

Similar to 7-14 Electrocomp Corporation manufactures two electrical product ir tu The assembly process for each is similar in that both require a certain amount of wiring fans. and drilling Each air conditioner takes 6 hours of wiring and 2 hours of drilling. Each fan must so through 2 hours of wiring and 1 hours of drilling. During the next production period, 240 hours of wiring time are available and up to 100 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembles may be sold for a $15 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 graph approach. Similar to 12-22 Fred Ridgeway has been given the responsibility of managing a training and development program. He knows the earliest start time, the latest start time, and the total costs of each activity. The information is given in the table. (The Latest start time is not given since you are not being asked to determine the budget based on that.) Using earliest start times, determine Fred's total monthly budget. Construct a full table to show the correct budget. (This takes up space so start on the left and use both pages.) Activity ES LS Time TOTAL (months) (months) COST ($1,000s) 12 12 610 12 5.5 15 15 -12 20 14 1814 20- 18

Answer 1

Similar to 7-12

Let the decision variables be

Number of air conditioners = X1

Number of fans = X2

Objective function

Maximize 25X1 + 15X2

Subject to constraints

6X1 + 2X2 <= 240

2X1 + 1X2 <= 100

X1, X2 >= 0

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The corner points are

(0,0)

(0,100)

Crossing point between the two constraint lines

(40,0)

Solving the crossing point between the two line is at X1 = 20 and 60. This means the objective function value at each corner points are

At (0,0) = 0

At (0,100) = 25*0 + 15*100 = 1500

At (20,60) = 25*20 + 15*60 = 1400

At (40,0) = 25*40 + 15*0 = 1000

Since it is a maximization problem, the maximum value is 1500 at the corner point (0,100). The optimal solution is 0 air conditioner and 100 fans to be produced with a maximum profit of 1500.