At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . , the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the price of $2.50 per kg. He leaves the rest of the grapes in storage where each day they dry out a little so that their weight decreases by 3%. Let wn be the weight (in kg) of the stored grapes at the beginning of day n for n ≥ 1 (before he takes any to the market). (a) Find the value of wn for n = 2. (b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.) (c) Let rn be the total revenue (in dollars) earned from the stored grapes from the beginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursive formula for rn. (d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num where num is entered by the user, and display the values in three columns: n, wn, rn with appropriate headings. Run the program for num = 20. (Use format bank.) (e) Use your MATLAB program to determine how many days it will take to sell all of the grapes
At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . ,
the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the price
of $2.50 per kg. He leaves the rest of the grapes in storage where each day they dry
out a little so that their weight decreases by 3%. Let wn be the weight (in kg) of
the stored grapes at the beginning of day n for n ≥ 1 (before he takes any to the
market).
(a) Find the value of wn for n = 2.
(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)
(c) Let rn be the total revenue (in dollars) earned from the stored grapes from the
beginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursive
formula for rn.
(d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num where
num is entered by the user, and display the values in three columns: n, wn, rn
with appropriate headings.
Run the program for num = 20. (Use format bank.)
(e) Use your MATLAB program to determine how many days it will take to sell
all of the grapes
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