Please help on this problem, I need detail solution as I was not abble to look a
ID: 325240 • Letter: P
Question
Please help on this problem, I need detail solution as I was not abble to look at it on the other solutions because are really small
The management of MACU Corporation is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability:
Department
Product (hours/unit)
1 2
Labor-Hours Available
A
1.00 0.38
110
B
0.25 0.30
45
C
0.25 0.45
60
Profit contribution/unit
$30.00 $15.00
What are the optimal (maximum profit) production quantities for the company?
a. What type/s of model/s should be used to solve the problem and why would you use that model/s? (20 points)
b. Develop a model of the MACU Corporation problem. Solve the model to determine the optimal product quantities of products 1 and 2. (60 points)
c. In computing the profit contribution per unit, management did not deduct labor costs because they are considered fixed for the upcoming planning period. However, suppose that overtime can be scheduled in some of the departments. Which department would you recommend scheduling for overtime? How much would you be willing to pay per hour of overtime in each department?
(20 points)
d. Suppose that 10, 6, and 8 hours of overtime may be scheduled in departments A,
B, and C respectively. The cost per hour of overtime is $17 in department A,
$21.50 in department B, and $10 in department C. Formulate a model that can be used to determine the optimal production quantity if overtime is made available. What are the optimal product quantities? What is the revised total contribution to profit? How much overtime do you recommend using in each department? What is the increase in the total contribution to profit if overtime is used?
(60 points)
Department
Product (hours/unit)
1 2
Labor-Hours Available
A
1.00 0.38
110
B
0.25 0.30
45
C
0.25 0.45
60
Profit contribution/unit
$30.00 $15.00
Explanation / Answer
1. Here the Linear Programming Model should be used to solve the problem . We will use this method because this is the most suitable option which will allow us to express the desired result which is maximizing profits in simple linear equation after taking into account all the constrainst which here are labor hours available for each department A, B & C. 2. Let us write the linear equation and express the constraints. Linear Equation is Maximize Profits = 30*N + 15*M Here 30 is profit contribution on Product 1 & 15 is the profit contribution on product 2 N is the number of optimum number of units of Product 1 to be produced M is the number of optimum number of units of Product 2 to be produced Constraints are : 1*N+0.38*M=110 0.25*N+0.35*M=45 0.25*N+0.45*M=60 Here 1 is the hours per unit for product 1 in department A , 0.38 is the hours per unit for product 2 in department A 0.25 is the hours per unit for product 1 in department B & 0.35 is the hours per unit for product 2 in department B 0.25 is the hours per unit for product 1 in department C & 0.45 is the hours per unit for product 2 in department C Now let us make use of excel for solving this problem : OPTION X Producing only N Production Quantity N 110 M 0 Product 1 Product 2 Production of N Production of M Time consumed for product 1 Time consumed for product 2 Total time consumed in each department Time constraint Profit Contribution for Product 1 Profit Contribution for Product 1 Optimum Profit Department Unit per hour Unit per hour Units Units hours hours hours hours USD/Unit USD/Unit D E F G H=D*F I=E*G J=H+I K L O P=L*F+O*G A 1 0.38 110 0 110 0 110 110 30 15 3300 B 0.25 0.35 110 0 27.5 0 27.5 45 C 0.25 0.45 110 0 27.5 0 27.5 60 OPTION Y Producing only M Production Quantity N 0 M 128 Product 1 Product 2 Production of N Production of M Time consumed for product 1 Time consumed for product 2 Total time consumed in each department Time constraint Profit Contribution for Product 1 Profit Contribution for Product 1 Optimum Profit Department Unit per hour Unit per hour Units Units hours hours hours hours USD/Unit USD/Unit D E F G H=D*F I=E*G J=H+I K L O P=L*F+O*G A 1 0.38 0 128 0 48.64 48.64 110 30 15 1920 B 0.25 0.35 0 128 0 44.8 44.8 45 C 0.25 0.45 0 128 0 57.6 57.6 60 OPTION Z Producing equal quantities of N & M Production Quantity N 75 M 75 Product 1 Product 2 Production of N Production of M Time consumed for product 1 Time consumed for product 2 Total time consumed in each department Time constraint Profit Contribution for Product 1 Profit Contribution for Product 1 Optimum Profit Department Unit per hour Unit per hour Units Units hours hours hours hours USD/Unit USD/Unit D E F G H=D*F I=E*G J=H+I K L O P=L*F+O*G A 1 0.38 75 75 75 28.5 103.5 110 30 15 3375 B 0.25 0.35 75 75 18.75 26.25 45 45 C 0.25 0.45 75 75 18.75 33.75 52.5 60 OPTION W Producing More of N & Less of M Production Quantity N 82 M 70 Product 1 Product 2 Production of N Production of M Time consumed for product 1 Time consumed for product 2 Total time consumed in each department Time constraint Profit Contribution for Product 1 Profit Contribution for Product 1 Optimum Profit Department Unit per hour Unit per hour Units Units hours hours hours hours USD/Unit USD/Unit D E F G H=D*F I=E*G J=H+I K L O P=L*F+O*G A 1 0.38 82 70 82 26.6 108.6 110 30 15 3510 B 0.25 0.35 82 70 20.5 24.5 45 45 C 0.25 0.45 82 70 20.5 31.5 52 60 OPTION V Producing less of N & more of M Production Quantity N 72 M 77 Product 1 Product 2 Production of N Production of M Time consumed for product 1 Time consumed for product 2 Total time consumed in each department Time constraint Profit Contribution for Product 1 Profit Contribution for Product 1 Optimum Profit Department Unit per hour Unit per hour Units Units hours hours hours hours USD/Unit USD/Unit D E F G H=D*F I=E*G J=H+I K L O P=L*F+O*G A 1 0.38 72 77 72 29.26 101.26 110 30 15 3315 B 0.25 0.35 72 77 18 26.95 44.95 45 C 0.25 0.45 72 77 18 34.65 52.65 60 Now as we can see from all of the above options , option W is best. I am finishing off here as the question is lengthy . Will attempt part c & d if question again comes back to me.
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