Quantitative Analysis for Business Decisions Number of consulting days 0 1 3 4 5 Company A Course 0 200 400 600 800 1000 Accounting Finance Marketing Statistics Company B 10 Table 15.22 Consulting charges ($'000) Expected grade for hours of study time 0 350 500 650 750 850 20 30 40 G HHSC HOCC HOHG OOOH G Company C 10 300 550 650 750 900 Legend O = Outstanding; H = Honours; G = Good; S = Satisfactory Table 15.23 For each course 5 points are given for an O; 4 for a H; 3 for a G; and 2 for an S. Determine how Margaret should budget her studying time if she wishes to maximise her expected total grade points. If she spends less than 10 hours on a course, she will fail it. Using dynamic programming, solve this problem, assuming that Margaret must not fail any course. 5. A firm allocates 4 units of a certain resource to 3 different activi- ties yielding profits according to Table 15.24. Using dynamic programming, determine a resource alloca- tion that maximises profits. Activity 123 Dynamic programming 0 1 2 0 3 0 OOO 45 5 0 0 Number of crates Units of resource 2 3 1 8 18 936 Table 15.24 three stores. Therefore, the owner wishes to know how he should allocate the five crates to the three stores to maximise expected profit. 867 For administrative reasons, the owner does not wish to split crates between stores. Also, he will distribute at least one crate to each store. Table 15.25 gives the estimated profit at each store, given an allocation of various numbers of crates. 1 0 13 17 19 110 123 Store 2 22 9 0 15 110 115. 115 115 8 Table 15.25 4 24 12 10 3 0 14 16 110 120 120 Use dynamic programming to determine how many of the five crates should be assigned to each of the three stores in order to maximise the total expected profit. 7. Wendy BBQ Chicken has four outlets operating in the metro- politan area. Staffing for the four outlets is managed centrally. Profit at each outlet is a function of the number of staff working, as shown in Table 15.26. Each outlet needs at least two persons. Use dynamic pro- gramming to determine the optimal staff assignment if 14 per- sons are available. 8. The Automotive Product Inc. produces a certain product in suf- ficient quantity to meet contracted sales in the next four months. 389