Diversified Ralph is a three-product firm, complete with lots of details. The products vary in terms of direct labor and direct material requirements, but also in terms of how many units are manufactured in a given batch (which determines the number of costly setups), their "complexity," and in terms of their material handling transactions. Direct labor (DL) and direct material (DM) costs are displayed below, along with the setup, complexity and handling measures.

The table is almost self-explanatory. One unit of product one requires $1300 of direct labor and $300 of direct material. The standard batch size is 300 units and consequently, production of q1 requires q1/300 units of setups. Each unit requires the equivalent of one unit of complexity and 12 transaction handlings.

In turn, four overhead pools are present. Their LLAs are given by: OV1 = 400,000 + 0.9DL,

OV2 = 200,000 + 0.4DM + 4T,

OV3 = 1,500, 000 + 0.0U, and

OV4 =30, 000S.

OV1 includes the various direct labor-related costs, such as fringe benefits and supervision. OV2 contains various direct-material related costs, including purchasing, receiving, inventory control and material handling. Notice the synthetic variables are direct material cost and an index of the number of material transactions, T. OV3 contains various product and process engineering costs. These costs are thought to be related to product complexity, as measured by the above noted complexity units tally. And OV4 collects various setup costs.

(a) Suppose q1 = 2,700,q2 = 2,400 and q3 = 1,800 units are produced, i.e., q = [2,700, 2,400, 1,800], and costs turn out to be precisely as detailed above, and thus total 17,707,800.

Determine the unit cost of each product, assuming the overhead pools are aggregated and allocated on the basis of direct labor cost.

(b) Repeat using separate overhead pools and the noted synthetic variables. For the OV2 pool where two such variables are present, allocate the pool on the basis of variable cost in that pool, i.e., 0.4DM + 4T

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direct labor (DL) direct material (DM) setups (S) complexity units (U) handling transactions (T) 9₁ 1300 300 9,/300 1 12 92 440 160 9/200 3 50 9₁ 400 960 9/600 2 20 direct labor (DL) direct material (DM) setups (S) complexity units (U) handling transactions (T) 9₁ 1300 300 9,/300 1 12 92 440 160 9/200 3 50 9₁ 400 960 9/600 2 20