Quality Air Conditioning manufactures three home air conditioners: an economy no
ID: 442620 • Letter: Q
Question
Quality Air Conditioning manufactures three home air conditioners: an economy nodel, a standard model, and a deluxe model. The profits per unit are: $65 for the ecnnomy model, $95 for the slandard model, and $135 for the deluxe model. The production requiremals are as follows Number of Manufacturing Time (hours Munber of Fans Cooling Coils Economy Model Standard Model Deluxe Model 12 14 of manufacturing time available, How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for this problem is as follows MAX 65E+958+135D IE +1S+IDs 200 1E +23 14D s 320 8E + 128+ 14D s 2400 Manufacturing time E,S,D20 Fans Cooling coils The optimal solution using EXCEL Solver is shown on the next page. Inclúded are the Answer Report, the Sensitivity Report, and the Limits Report. The following page has questions you must answer concerning your interpretation of the solution output.Explanation / Answer
5. Looking at the sensitivity report – Adjustable section,
We see that for Economy, allowable increase is $10. This implies that if the profit is increased by upto $10, the number of units of Economy, Standard and Deluxe would remain the same. Thus, if we increase the profit from $65 to $70 or a $5 increase, this is within range and thus number of units of Economy, standard and deluxe would still remain as 80,120 and 0 respectively. However, total profit will increase and will be equal to:
Profit = $(70*80 + 95*120 + 135*0) = $17000
6. From sensitivity report adjustable section we see that:
Allowable increase for 3 models are as follows: Economy:$10, Standard:$35, Deluxe:$20
As the profit increase provided in the question are within range for all 3, the optimal number of units will still remain as: Economy-80, Standard-120, Deluxe-0
New profit/unit for 3 models are: Economy - $71, Standard - $97, Deluxe - $137
Total profit = $(71*80 + 97*120 + 137*0) = $17320
7. From the Constraints part of the sensitivity report, we see
Shadow price for Fans is $35 and allowable increase is 80. Now shadow price is the increase in profit for every unit increase in the constraint upto the allowable unit. So in this case we can increase the constraints on the number of fans upto 200+80 = 280 and there will be a $35/unit increase in total profit.
As the increase in number of fans is 50, thus increase in total profit = $35*50 = $1750
Thus, new profit = $16600+$1750 = $18350
The optimal solution of number of units of economy, standard and deluxe model will change as the size of the feasible range changes. To get the new optimal solution, the solver has to be run again.
In this case, if we run the solver, we get Economy = 180, Standard = 70, Deluxe =0
8. The allowable increase for cooling coils is 80. Thus, if the increase is 100, dual price will change.
9. I would not purchase. My profit in this case would be from answer no.7: $18350-$(50*35) = $16600 which is the same as if I do not purchase these 50 fans. Thus, I would not purchase.
10. I would not purchase 100 cooling coils for $30. This reduces my profit by 100*30 = $3000. If I had to internally increase my capacity, my profit would be larger. Thus, I would not purchase.