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Throughput Accounting/Linear Programming

Customer Question

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Submitted: 11 years ago.
Category: Homework
Expert:  xarqi replied 11 years ago.
What is your question?
Customer: replied 11 years ago.
Reply to xarqi's Post: Hi, well, this is like a case analysis. So all details are here. The question I'm trying to get help for is this situation (resource flexibility)- It all is part of the case I've placed below the situation:As you'll see below it states that there are 3 questions. This is what I'm looking for help with:
Operating situation(Resource flexibility)
The firm would like its existing resources to be more flexible. The company would train its workers and would modify its machines so that they could work on all four products. The total available resources do not change, but the labor and machine constraints do change to reflect this new flexibility. The market constraints remain on all four products. What would the company's throughput be now with the new labor and machine constraints? Which resource is the constraint in this situation? How much profit would the firm make? How would you use the information in this situation to determine if the company should go ahead with the investment required to train its workers and to modify its machines?
Constraints:
(1) labor hours
(2) machine hours
(3) market
A < 2000
B < 2000
C < 2000
D < 2000

PREMIER PRODUCTS, INC. - TOC
Introduction
These notes convert the Premier Products case from a cost-based case to a throughput-based case. You should review the original Premier Products case. The information in the case is used to make this transformation. Five operating situations have been identified. In each situation the same throughput equation is maximized subject to the specific constraints for that situation using standard linear programming techniques. The objective is to find the mix of products that provides the most throughput for the company.   
Definition of throughput
Throughput for a specific product is calculated by taking the difference between the selling price of the product and the cost of all parts that must be purchased from external suppliers for the product. Throughput represents the money that the company gets to keep to pay the cost of all of its resources. The throughput for each of the products is its selling price minus its material cost.
Throughput equation
Maximize 83A + 33.5B + 49.5C + 44D
Assumptions
This analysis assumes that the variable overhead listed in Table A of the original case represents the cost of using a machine to produce the four products. It is also assumed that the cost of all machines is the same $20 per hour. For example, the variable overhead for product A is $15 per unit. If the $15 represents product A's use of a machine and the machine costs $20 per hour, then one unit of product A uses 3/4 (.75) of a machine hour [$15 per unit divided by $20 per hour]. Product B has a unit variable cost of $7.50 per unit. This works out to 3/8 (.375) of a machine hour for each unit of product B. Each unit of product C uses 1/4 of a machine hour, and one unit of product D uses 3/8 of a machine hour. In Table A the cost of direct labor for product A is given as $30 per unit. Because each unit of A requires 6 direct labor hours, this makes the rate $5 per hour. This rate is the same for products B, C, and D.
The original case states that 1,000 units of each product can be produced or a maximum amount of 2,000 units of A or B and a maximum of 2,000 units of C or D. This infers that labor and machines can only produce either A and B or C and D. The existing labor and machines cannot produce all four products. If 2000 units of A are produced and if each unit of A requires 6 labor hours, then the firm must have 12,000 direct labor hours available to work on products A and B. If the firm can produce 2000 units of C, then the firm must have 6,000 labor hours available for products C and D. [NOTE: These labor hour figures differ from those in the original case.] The maximum number of machine hours for products A and B is 1,500 because each unit of product A requires 3/4 of an hour and 2,000 units can be produced. The maximum number of machine hours for C and D is 750 machine hours because each unit of product D requires 3/8 of an hour and 2,000 units can be produced.
Customer: replied 11 years ago.
Hello, can you please let me know if you can help with this problem?

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