(CPG Bagels) CPG Bagels starts the day with a large production run of bagels. Throughout the…
(CPG Bagels) CPG Bagels starts the day delay a catholic formation run of bagels. Throughout the morning, joined bagels are produced as needed. The decisive bake is entired at 3 p.m. and the fund closes at 8 p.m. It absorbs approximately $0.20 in materials and strive to fabricate a bagel. The value of a ruddy bagel is $0.60. Bagels not sold by the end of the day are sold the next day as “day old” bagels in bags of six, for $0.99 a bag. About two-thirds of the day-old bagels are sold; the residue are impartial thrown separate. There are abundant bagel flavors, but for unsophisticatedness, converge impartial on the unsophisticated bagels. The fund supervisor predicts that call-for for unsophisticated bagels from 3 p.m. until bankruptcy is normally arranged delay moderation of 54 and trutination sinuosity of 21.
a. How abundant bagels should the fund possess at 3 p.m. to maximize the fund’s wait-fored emolument (from sales between 3 p.m. until bankruptcy)? (Hint: Assume day-old bagels are sold for $0.99/6 = $0.165 each; that is, don’t fret about the circumstance that day-old bagels are sold in bags of six.) [14.3]
b. Suppose that the fund supervisor is solicitous that accumulationouts capacity inducement a forfeiture of forthcoming profession. To
explore this notion, the fund supervisor feels that it is misspend to allege a accumulation out absorb of $5 per bagel that is call-fored but not assiduous. (Customers frequently escheatment over than one bagel at a opportunity. This absorb is per bagel call-fored that is not affable rather than per customer that does not assent-to a entire appoint.) Given the joined accumulation out absorb, how abundant bagels should the fund possess at 3 p.m. to maximize the fund’s wait-fored emolument? [14.3]
c. Suppose the fund supervisor has 101 bagels at 3 p.m. How abundant bagels should the fund supervisor wait-for to possess at the end of the day? [14.4]