Chapter 11.1, Problem 9P

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 priceof $2.50 per kg. He leaves the rest of the grapes in storage where each day they dryout a little so that their weight decreases by 3%. Let wn be the weight (in kg) ofthe stored grapes at the beginning of day n for n ≥ 1 (before he takes any to themarket).(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 thebeginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursiveformula for rn.(d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num wherenum is entered by the user, and display the values in three columns: n, wn, rnwith appropriate headings.Run the program for num =…

Consider the following model of trade between Home and Foreign. Assume throughout that those two countries are the only two countries in the world, at least for purposes of trade. There are two goods: Corn and Radio. Consumers always spend one-third of their income on Corn and the remainder on Radios. The only factor of production is labour. Each home country worker can produce 2 units of Corn or 3 units of Radios per unit of time, while each foreign worker can produce 2 units of Corn or 4 units of Radios per unit of time. There are 30 workers in Home and 60 workers in Foreign. Draw the production possibility frontier for each country (put Corn on the vertical axis and Radios on the horizontal axis).

[Very Hard] Suppose, you are working in a company ‘X’ where your job is to calculate the profit based  on their investment.  If the company invests 100,000 USD or less, their profit will be based on 75,000 USD as  first 25,000 USD goes to set up the business in the first place. For the first 100,000 USD,  the profit margin is low: 4.5%. Therefore, for every 100 dollar they spend, they get a profit  of 4.5 dollar. For an investment greater than 100,000 USD, for the first 100,000 USD (actually on 75,000  USD as 25,000 is the setup cost), the profit margin is 4.5% where for the rest, it goes up to  8%. For example, if they invest 250,000 USD, they will get an 8% profit for the 150,000  USD. In addition, from the rest 100,000 USD, 25,000 is the setup cost and there will be a  4.5% profit on the rest 75,000. Investment will always be greater or equal to 25,000 and  multiple of 100. Complete the RECURSIVE methods below that take an array of integers (investments)  and an iterator (always…