Question: Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit

Problem 3-12 (Algorithmic) Quality Air

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $97, and $133, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 2 12 Deluxe 1 4 14 For the coming production period, the company has 350 fan motors, 340 cooling coils, and 2000 hours 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 the problem is as follows: Max 63E + 975 + 133D s.t. 1E + 1S + 1D s 350 Fan motors 1E + 2S + 4D S 340 Cooling coils 8E + 12S + 140 s 2000 Manufacturing time E,S, D20 The computer solution is shown in the figure below. Optimal Objective Value = 16660.00000 Variable E Value ----------------- 180.00000 0.00000 Reduced Cost ------------ 0.00000 S -2.55556 Optimal Objective Value = 16660.00000 Variable E Value 180.00000 0.00000 40.00000 Reduced Cost 0.00000 -2.55556 0.00000 S D Constraint 1 Slack/Surplus 130.00000 0.00000 0.00000 Dual Value 0.00000 10.11111 6.61111 2 3 Variable Allowable Decrease E Objective Coefficient 63.00000 97.00000 133.00000 Allowable Increase ---------- 13.00000 2.55556 119.00000 S 2.30000 Infinite 11.50000 D Constraint RHS Value 350.00000 340.00000 Allowable Increase Infinite 231.42860 720.00000 Allowable Decrease ----------- 130.00000 90.00000 1 2 3 2000.00000 810.00000 a. What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nearest whole number. If your answer is zero, enter "O". Optimal Solution Economy models (E) Standard models (S) Deluxe models (D) Value of the objective function $ x b. Which constraints are binding? Fan motors: Binding X Cooling coils: Binding Manufacturing time: Binding C. Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number. Constraints Extra capacity Number of units Fan motors Yes X 0 X Cooling coils Yes 0 Manufacturing time No X 0 X d. If the profit for the standard model were increased to $112 per unit, would the optimal solution change? to $99.55556 . $112 is The optimal solution would not X change because the profit of the standard model can vary from $0 this range without the optimal solution changing

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related General Management Questions!

Read the Scenario Congratulations, you are now the Police Chief in Anytown, USA. A city with 30,000 residents and you are responsible to provide 24 hour a day police coverage. You have a total of 45...

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $69, 91, and $127,...

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $95, and $133,...

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $65, $97, and $139,...

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $95, and $133,...

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $69, $91, and $127,...

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $59, $89, and $137,...

Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $69, $91, and $127,...

Please fill out with the correct answer and I will definitely rate like/ thumb up. Thank you! Problem 3-13 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy...

Please show work. Thanks in advance. Problem 3-13 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits...

In proper General Journal format, record the transactions for the month; include descriptions of each transaction with your journal entry. Use only the accounts shown in the chart of accounts. Post...

How do profit and loss statements cash flow (using the direct and indirect methods), and aging summaries contribute to new budgets? How can you ensure that managers and supervisors in the...

To facilitate a bribery scheme, a fraudster might divert company funds to a non - company account from which the illegal payments can be made. This account is called a: a . Petty cash fund b . Slush...

What are the economic arguments to be considered for and against Fair Trade products?