CMA Study Group

Part 2 - Constraint Help

  • 1.  Part 2 - Constraint Help

    Posted 18 days ago
    Wiley says to use linear programming..? Is there any easier way to solve these problems about CM per constraint?

    The Mix and Match Company has two products, Product X and Product Y, that it manufactures through its production facilities. The contribution margin for Product X is $15 per unit while Product Y's contribution is $25. Each product uses Materials A and B. Product X uses three pounds of Material A while Product Y uses six pounds. Product X requires six feet of Material B and Product Y uses four feet. The company can only purchase 600 pounds of Material A and 880 feet of Material B. The optimum mix of products to manufacture would be:



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    Bradley Kilbreth
    Student
    Manchester NH
    United States
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  • 2.  RE: Part 2 - Constraint Help

    Posted 17 days ago
    okay, its very length question because you need to analyze many things.

    Lets first break down each option.
    1- producing 40 unit of X and 120 unit of Y
    40 units of X would consume 40*3= 120 A of total 600 - and 40*6= 240 B of total 880, which will produce a contribution of 40*15= 600 Dollar.
    120 Unit of Y would consume 120*6= 720 which is out of the company's ability, therefore, the total contribution produced from this option is 600.

    2- producing 0 units of X and 100 units of Y.
    0 units of X would consume nothing, therefore no contribution would be generated from X product.
    100 units of Y would consume 100*6=600 A of total 600 - and 100*40 = 400 B of total 880, producing total contribution from this option equal to 2500.

    3- producing 146 units of X and 0 units of Y.
    146 units of X would consume 146*3 = 438 A of total 600 - and 146*4 = 584 B of total 880. producing total contribution from this option equal to 2190.

    4- Producing 120 units if X and 40 units of Y.
    120 units of X would consume 120*3= 360 A of total 600 - and 120*4 = 480 B of total 880. producing contribution from this product equal to 1800.
    40 units of Y would consume 40*6 = 240 A of total 600 - and 100*4 = 400 of total 880. producing contribution from this product equal to 1000.
    Total contribution generated from selecting option D = 1800+100=2800 Which is optimum as total contribution and matching company ability to purchase the designated amount. The answer is D - Last selection.





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    Mohamed Shamsaldin
    Accountant
    Dammam
    Saudi Arabia
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  • 3.  RE: Part 2 - Constraint Help

    Posted 17 days ago
    unfortunately, there is no easier way to solve this "at least as I know so far" some materials just mentioned that in order to solve such a question you need analysis for each option to find out the true figure.

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    Mohamed Shamsaldin
    Accountant
    Dammam
    Saudi Arabia
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  • 4.  RE: Part 2 - Constraint Help

    Posted 17 days ago
    Dear Bradely, 

    The last option provides the maximum CM by using the maximum allowed purchase of both the Materials. 

    CM of 2800.
    I had checked all the options, and found out the greatest CM & also checked whether its permitted by the maximum limit of raw materials. There will be other direct options as well to find the same answer. 





  • 5.  RE: Part 2 - Constraint Help

    Posted 17 days ago
    Yes.  For this type of problem, glance at the extremes first.  Answer C will likely be the lowest total because the CM is lower.  Answer B will be a higher total because the CM is larger (by $10 per unit) even though the units produced are somewhat less.  Answer A will not be possible for the pounds calculation on Product Y.  Then, you are left with calculating Answer D to see if it maximizes total CM and meets the pounds and feet limitations.

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    Mark Freudenberg CPA
    Chief Financial Officer
    Dublin OH
    United States
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  • 6.  RE: Part 2 - Constraint Help

    Posted 17 days ago
    The key to this is the restraints
    X
    15 CM
    3 lb of A
    6' of B

    Y
    25 CM
    6 lb of A
    4' of B

    Max A 600 lb/ 6 prod Y = 100 max

    Max B 880' / 6 prod x = 130 max

    When you look at the possible answers you see that the two in the middle aren't possible because of the constraints. If you start to multiply the first choice, it goes over the constraint for A. (40x3) + (120x6) =840. That leaves D as the only possible answer.

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    Judi Aldridge
    Accountant
    Philadelphia PA
    United States
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