The Esna Fabricating Company manufactures valves, faucets, and similar items under contract for various industrial and commercial clients. Whenever the company has no special jobs to do, it uses its labor force and plant to produce a line of faucets which it sells to a distributor for eventual sale in hardware stores. Esna can produce 5,000 of these faucets weekly, on average, and sells them for $1.65 per unit, this representing a 50 percent markup over variable costs. This production is suspended whenever Esna wins a more lucrative contract, however. Esna is currently considering bidding for a contract to manufacture several very large pressure valves for use in the pulp-making industry. It has estimated the costs associated with this job as fol¬ lows:

In addition to the above, Esna has incurred $850 in expenses to acquire the detailed specifications for examination prior to submitting its bid. If the contract is won, Esna expects to incur another $2,500 for design costs before beginning manufacture of the valves, and the man¬ ufacturing process is expected to take 300 labor hours, or three weeks of the plant’s time. No new direct labor will need to be hired for the job, since the regular labor force (diverted from faucet production) is expected to be sufficient to handle the job.
Esna’s bidding policy is to mark up incremental costs of each job such that the expected value of contribution is maximized. An examination of the outcomes of over 300 jobs bid for in the past two years indicates that the probability of winning the contract is related to the ratio of the bid price to incremental cost, for each particular contract, in the following wray:
P = 2.825 - 0.115R - 1A21R2 where P is the success probability and R is the ratio of the bid price to the incremental costs of each job tendered for.

(a) What are the probabilities of winning the contract at markups of 10 percent, 15 percent, 20 percent, 25 percent, and 30 percent, respectively?

(b) What price should Esna submit?

(c) Outline any reservations or qualifications you may have concerning your recommended bid price.

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Direct labor (300 labor hours @ $20) Direct materials Variable overhead expenses Allocated overheads (150% of direct labor) $6,000 8,650 4,270 9,000