Malkin Company has three divisions (R, S, and T), organized as decentralized profit centers. Division R produces the basic chemical Randine (in multiples of 1,000 pounds) and transfers it to Divisions S and T. Division S processes Randine into the final product Syntex, and Division T processes Randine into the final product Termix. No material is lost during processing. Division R has no fixed costs. The variable cost per pound of Randine is $ 0.18.

Division R has a capacity limit of 10,000 pounds. Divisions S and T have capacity limits of 4,000 and 6,000 pounds, respectively. Divisions S and T sell their final product in separate markets. The company keeps no inventories of any kind.

The cumulative net revenues (i. e., total revenues (-) total processing costs) for divisions S and T at various output levels are summarized below.

Required
1. Suppose there is no external market for Randine. What quantity of Randine should the Malkin Company produce to maximize overall income? How should this quantity be allocated between the two processing divisions?
2. What range of transfer prices will motivate Divisions S and T to demand the quantities that maximize over-all income (as determined in requirement 1), as well as motivate Division R to produce the sum of those quantities?
3. Suppose that Division R can sell any quantity of Randine in a perfectly competitive market for $ 0.33 a pound. To maximize Malkin’s income, how many pounds of Randine should Division R transfer to Divisions S and T, and how much should it sell in the external market?
4. What range of transfer prices will result in Divisions R, S, and T taking the actions determined as optimal in requirement 3? Explain youranswer.

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Division S 1,000 Total Net Revenues (S) from Sale of Syntex500 4,000 $1,200 Pounds of Randine Processed in S 2,000 3,000 850$1,100 1,000 $ 600 Division T 2,000 $1,200 3,000 $1,800 5,000 $2,250 6,000 $2,350 Pounds of Randine Processed in T 4,000 $2.100 Total Net Revenues ($) from Sale of Termix