Please solve only the first question the other two questions are just the questions asks to solve question 1

(30 points) Joy and Kim have normal 9-5 jobs during the week. On the weekends, they have a side hustle where they make wooden toys and sell them on Etsy. Joy does the woodwork, and then Kim paints the toys. Joy can work at most 4 hours over the weekend, and Kim can work at most 6 hours over the weekend. Production data is below Joy and Kim are trying to determine what to produce on an average weekend to maximize their profit. Formulate a linear program for this problem. Clearly define your decision variables and any indices/parameters that you use. Also, be sure to write out your objective function and constraints "in words" and "in math". Do not solve the LP. 5. (30 points) A company produces widgets at its two factories, one in Atlanta and the other in Chicago. The company sells to four primary customers, who are located in Boston, Dallas, St. Louis, and Tampa. Below are the distances (in miles) from the factories to the customers. The Atlanta factory can produce up to 180,000 widgets per year, while the Chicago factory can produce up to 220,000 widgets per year. The annual widget demand by customer is below. Your task is to decide how to fulfill the customer demand to minimize the total distance that widgets travel from factories to customers. If an order of two widgets travels 50 miles, this gives a total of 250=100 miles traveled. For this problem, we are assuming that the total distance traveled is a reasonable proxy for the transportation cost. Formulate a linear program for this problem. Clearly define your decision variables and any indices/parameters that you use. Also, be sure to write out your objective function and constraints "in words" and "in math". Do not solve the LP. 1. (30 points) Write Python code for the mathematical models of questions 4 and 5