Question

Part c, d and e

You pay your secretary $6.75 per hour. A stamped envelope costs 42 cents, and regular stationery costs 5 cents per page, but fancy letterhead stationery costs 16 cents per page. Assume that a letter requires fancy letterhead stationery for the first page but that regular paper will suffice for the rest of the letter. (Round your answers to the nearest cent.) (a) How much does the stationery alone cost for a 9-page letter? $ .56 (b) How much does it cost to prepare and mail a 9-page letter if your secretary spends 4 hours on typing and corrections? $ 27,98 (c) Use a formula to express the cost of the stationery alone for a letter as a function of the number of pages in the letter. (Let c be the cost in dollars of the stationery and p the number of pages.) cp) = (d) Use a formula to express the cost of preparing and mailing a letter as a function of the number of pages in the letter and the time it takes your secretary to type it. (Let h be the number of hours spent typing the letter, let p be the number of pages of the letter, and let C be the cost in dollars of preparing and mailing the letter.) cih, p) = (e) Use the function you made in part (d) to find the cost of preparing and mailing a 4-page letter that it takes your secretary 35 minutes to type. $

Answer 1

a). A 9-page letter would have its 1^st page as the fancy letter head and 8 pages of regular stationery.

Therefore, the stationery cost alone for a 9-page letter   is 1*0.16+8*0.05 = $ 0.56.

(b). If the secretary spands 4 hours on typing and corrections, then the amount payable to the secretary is 4* $ 6.75 = $ 27.00. On adding the cost of the envelope and the stationery, the total cost of preparing and mailing the letter is $ 0.56 + $ 0.42+$ 27 = $ 27.98.

( c). If c is the cost in dollars of the stationery and if p is the number of pages, then c(p) = 0.16+(p-1)*0.05 = 0.16+0.05p – 0.05 = 0.05p+0.11. Thus, c(p) = 0.05p+0.11.

( d). Let h be the number of hours spent by the secretary in preparing a p-page letter. Then c(h,p) = 6.75h + 0.42+ 0.05p+0.11= 6.75h+0.05p + 0.53. Thus, c(h,p) = 6.75h+0.05p + 0.53.

(e). The cost of preparing and mailing a 4-page letter which took the secretary 35 minutes of prepare, is 6.75*(35/60)+0.05*4+0.53 = 3.94 +0.20+0.53 = $ 4.67.