Hart manufacturing makes three products. each product requires manufacturing operations in three departments: a, b, and c. the labor-hour

Question

Hart Manufacturing produces three products, each requiring operations in three departments: A, B, and C. The labor-hour requirements by department for each product are as follows:

Department A: 
Product 1: 1.95 hours 
Product 2: 3.45 hours

Product 3: 2.45 hours

Department B:

Product 1: 2.90 hours 
Product 2: 1.90 hours

Product 3: 3.40 hours

Department C:

Product 1: 0.70 hours 
Product 2: 0.70 hours 
Product 3: 0.70 hours

During the next production period, the available labor-hours are 540 in Department A, 440 in Department B, and 140 in Department C. The profit contributions per unit are as follows: $34 for Product 1, $37 for Product 2, and $39 for Product 3. 
Please formulate a linear programming model to maximize the total profit contribution. For any boxes where you need to enter subtractive or negative numbers, use a minus sign (e.g., -300). Let ( p_i ) represent the units of product ( i ) produced.

Anonymous · Accepted Answer

Max : $34X + $37y + $39Zsubject to:1.95X + 3.45Y + 2.45Z ≤ 5402.90X + 1.90Y +3.40Z ≤ 440 0.70X + 0.70Y + 0.70Z ≤ 140X ≥ 0 , Y ≥ 0 , Z ≥ 0Step-by-step explanation:Represent product 1 by X, product 2 by Y and product 3 by Z

Anonymous · Answer

Missing Part of the Question The management also stated that we should not consider making more than 175 units for product 1, 150units of product 2, or 140 units of product 3.Answer and Explanation:GivenDepartment Product 1 Product 2 Product 3A 1.50 3.00 2.00B 2.00 1.00 2.50C 0.25 0.25 0.25The profit contributions per unit areProduct 1 = $25 Product 2 = $28product 3 = $30The set up costs areProduct 1 = $400Product 2 = $550Product 3 =$600 The labor-hours available are Department A = 450 Department B = 350Department C = 50Formulating a linear programming model, as haveLet X be the number of units producedMax Z = 25X1 + 28X2 + 30X3 - 400Y1 - 550Y2 - 600Y3Subjected to (the constraints are)1.5X1 + 3X2 + 2X3 ≤ 4502X1 + X2 + 2.5X3 ≤ 350 0.25X1 + 0.25X2 + 0.25X3 ≤ 500 ≤ X1 ≤ 175Y10 ≤ X2 ≤ 150Y20 ≤ X3 ≤ 140Y3The first three constraints represents the labour hours in departments A, B and C.While the last three constraints represents the maximum production of product 1,2 and 3.

Anonymous · Answer

The solution is given in the pictures attachedExplanation:complete question(a)Formulate a linear programming model for maximizing total profit contribution.If the constant is "1" it must be entered in the box. If required, round your answers to two decimal places.Let Pi = units of product i produced(b)  Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution(c)   After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $550 for product 2, and $600 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution after taking into account the setup costs?(d)Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs provided in part (c) into account. Management also stated that we should not consider making more than 175 units of product 1, 150 units of product 2, or 140 units of product 3. What are the new objective function and additional equation constraints?If the constant is "1" it must be entered in the box.Let Yi is one if any quantity of product i is produced and zero otherwise.(e)Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c).If required, round your answers to nearest whole number. If your answer is zero enter “0”.

Anonymous

Hart manufacturing makes three products. each product requires manufacturing operations in three departments: a, b, and c. the labor-hour

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