Problem 1. Recall the problem 1 of homework 1, where a company produces lwo kinds of products. Producing one product of the first type requires 1/5 hours of assembly labor, 1/6 hours of testing, and $1.5 worth of raw materials. This type of product is sold at $9.3 each. Producing one product of the second type requires 1/4 hours of assembly, 1/4 hours of testing, and $1.4 worth of raw materials. This type of product is sold at $8.5 each. Currently, the company can provide at most 90 hours of assembly labor and 80 hours of testing every day. Let x1 and x2 be the amount of the two types of products produced per day. To maximize the daily profit, we write down the following standard form LP problem: maximizex1,x2,x3,x1s.t.(9.31.5)x1+(8.51.4)x251x1+41x2+x3=9061x1+41x2+x4=80x1,x2,x3,x10 where x3 and x4 are slack variables. If we solve this problem with the simplex method, we will find that the optimal basis is B={1,4}, and optimal BFS is x=[450,0,0,5]. (1). If the price of the type 2 product changes from $8.5 to a new price. What is the range of the new price if this change in price does not result in a change in the optimal basis? (25 points.) (2). If the price of the type 1 product changes from $9.3 to a new price. What is the range of the new price if this change in price does not result in a change in the optimal basis? (25 points.) (3). Suppose the maximal amount of daily testing hours changes due to some reason. What is the range of new daily maximal testing hour if this change does not result in a change in the optimal basis? (25 points.) (4). Previously, the payment to the assembly and testing labor was already counted in the $1.5 raw material cost of for type 1 product and the $1.4 raw material cost of for type 2 product. Now suppose for both the assembly and testing labor, the company plan to provide an addition $(0) of payment per hour. What is the range of if this additional payment does not change the optimal basis? (25 points.)