14. second best Suppose we want to maximize f(x, y, z) = 6x − x2 + 9y − y2 + 5z − z2 − θxyz, subject to x, y, z ≥ 0.

(a) Let θ = 1. Determine the values of x, y and z that maximize f(x, y, z).

(b) Now suppose x = 3, y = 1 and z = 0. Is it an improvement to move z from z = 0 to z = 1, holding the other two variables constant? Why is it useful to move z away from its globally optimal setting?

(c) Now suppose x = 1, y = 4.5 and z = 2. Is it an improvement to move x from x = 1 to x = 0.

(d) Repeat

(a)

(b) and

(c) above for the case of θ = 0.

(e) Write a short paragraph detailing your findings and what this implies about connecting the costing system closer to the firm’s technology.

15. lots of details Numbing 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.

q1 q2 q3 direct labor (DL) 40 100 240 direct material (DM) 18 250 480 setups (S) q1/500 q2/500 q3/400 complexity units (U) 1 1 2 handling transactions (T) 12 5 20 In turn, four overhead pools are present. Their LLAs are given by:

OV1 = 750, 000 + 0.4DL,OV2 = 200, 000 + 0.2DM + 1.5T,OV3 =

750, 000 + 0.0U, and OV4 = 1, 500S. 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, 500, q2 = 2, 500 and q3 = 2, 400 units are produced, i.e., q = [2,500, 2,500, 2,400], and costs turn out to be precisely as detailed above, and thus total 5, 342, 550. 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., 0.2DM + 1.5T

(c) Repeat

(a) and

(b) for q = [2,500, 500, 2400], q = [5,000, 500, 5,200] and q = [2,500, 0, 0].

(d) We implicitly used a full costing approach in the above. What, using the modernism approach, is the variable cost per unit?