Need help with these 4 problems please, and with clear explanations as well.

For a certain company, the cost function for producing a items is C (x) = 40 % + 150 and the revenue function for selling & items is R (x) = -0.5(x - 110)- + 6,050. The maximum capacity of the company is 160 items. The profit function P(x) is the revenue function R (x) (how much it takes in) minus the cost function " (x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answers to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the profit function? P@)= sin [2) Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P (x)? Hint: Does calculating P (x) make sense when > = -10 or r = 1, 000? 3. The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose? Profit when producing 70 items = Number Profit when producing 80 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?\fA cube has an edge of 4 feet. The edge is increasing at the rate of 3 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed. Hint: Remember that the volume of a cube is the cube (third power) of the length of a side. ab % lal 11' sfuaa.) M 0 V (m) feet3 Use a system of linear equations with two variables and two equations to solve. 195 students enrolled in a freshman-level chemistry class. By the end of the semester, 4 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed. Passing Students: Number Failing Students: Number