9. accounting library and decision frame Ralph’s Library is a two product firm. Quantities of the two products are denoted q1 and q2. Ralph has studied the situation, and decided to rely on the following LLAs:

direct labor cost DL = 90q1 + 95q2 direct material cost DM = 50q1 + 100q2 first overhead pool OV1 = 400, 000 + 3(DL)

second overhead pool OV2 = 200, 000 + 1(DM);

selling and adm. S&A = 700, 000 + 10q1 + 20q2 In addition, Ralph estimates total revenue via TR = 860q1 + 960q2.

Ralph also faces capacity constraints. Machine hours are limited in each of two departments to a total of 6, 000. (Each department has a capacity of 6, 000 machine hours.) Machine hour requirements are as follows:

product 1 product 2 department one 1 2 department two 2 1 So, for example, a unit of the first product requires one machine hour in department one and two machine hours in department two.

(a) Determine Ralph’s optimal output and associated maximum profit.

(b) Summarize your recommendation in

(a) above with two income statements, one based on full costing and the other based on variable costing.

(c) Ralph’s Cousin, a meddling individual, insists product 2 is unacceptable on aesthetic grounds. Ralph decides to examine life on the assumption q2 = 0. What is Ralph’s opportunity cost of following the Cousin’s suggestion?

(d) Return to part

(a) above. Ralph now encounters a new customer.
This customer seeks a custom-made item. Ralph estimates this will require direct labor of 150 and direct material of 150. It will also require 2 machine hours in each department.
Ralph also is looking for the easy way out. Determine the cost of this modified product such that Ralph should oblige this customer if and only if the offered price
P is greater than cost.

(e) Suppose Ralph decides to oblige this new customer in

(d) above.
Further suppose output and the LLAs turn out just as expected.
Everything produced is sold, except the custom-made product for the new customer didn’t get shipped until the first day of the next fiscal year; it remains (fully completed) in inventory at year end. What inventory value will the accounting library place on this unit? Assume variable costing is used for this purpose.
Carefully explain why this cost recorded in the accounting library differs from that constructed in part

(d) above.

(f) Just for fun, return to part

(d) above. Formulate an optimization program that uses three products, the first two modeled in part

(a) above and the third the one referred to part (e), with a selling price of
P. Be certain to add the constraint 0 ≤ q3 ≤ 1.
Carefully explain why the cost associated with this third product differs from the cost associated with the same product in part

(d) above.