help me solve this, and how to solve the problems with the shown work?

1. System of inequalities /Linear Programming (1.1) (10 points) Graph the solution set for the system of inequalities. Shade the area that is the solution set. Show work for how you are graphing the first two inequalities. y y - x2-4 y + 2x - 5 x2 2 yo 6 4 2 2 8 -2- (1.2) (4 points) List the corner points of the solution set. Show work for finding any fractional points. Answer: (1.3) (4 points) Test the objective function 4x + 23y for each of the corner points. Find the minimum of the objective function 4x + 23y and the point at which it occurs. Minimum value: Point where it occurs:2. (6 points) A hardware store employee is paid a base salary of $2000 per month plus an 8% commission on sales over $7000. How much must the employee sell to earn $4000 for the month. Answer: 3. Tara starts a company designing ower bouquets. The materials cost $10 per bouquet of lilies and $25 per bouquet of roses. They can spend a maximum of $5,000 on buying materials needed for the decoration of the bouquets. The labor requirements are 0.6 hours per bouquet of lilies and 2 hours per bouquet of roses. They have a maximum of 300 labor hours. The prot for selling is $25 per bouquet of lilies and $30 per bouquet of roses. (3.1) (6 points) Write a system of linear inequali- Answer: tie; to model the production constraints. Use m to represent the number of bouquets of lilies and 'y to represent the number of bouquets of roses. Remember to include inequalities for the minimum number of items. (3.2) (2 points} Write the prot function, P using Answer: input variables a: and y. 4. A dietitian charges $100 for an hour of diet consulting and the cost to the business for 3: hours of consulting is given by C (at) 2 50:1: + 2000. (4.1) (4 points} Find the value of C(G). De- (42) (3 points) Write the prot function and scribe the meaning of this number with re- simplify it. Show work to support the an- spect to the scenario. swer. P(:c) = 0(6) = Meaning: (4.3) (1 point) What is the marginal prot? Answer (4.4) (6 points} After how many hours will the dietitian break even? (Round up to the nearest hour and include units.) Work: 5. For a certain product, the demand equation is Exp10g : 305 and the supply equation is 211+qu : 150. (5.1) (7 points) \"That is the market equilibrium point, ((1,1))? Answer: (5.2) (3 points) How many of the items will consumers demand at a price of $75? 5. Graph the following. Show as much of the graph as ts on the grid. (6.1) (8 points) (6.2) (8 points) 9(3) :2|:r+1| 9:73 x { 71 2 gm 5 y 4 3 5 y 2 4 1 3 I I I I I I l I I I ED 2 -5-43-2-1_112345 1 I _2 l I' l' I I I I I I' I > _3 -5 -4 3 2 -1_1 1 2 3 4 5 -4 -2 _5 -3 -4 -5 T. (8 points) Solve the following equation. Be sure to check that your answer{s) is/are in the domain. If not, cross an answer out and note it. is not in the domain. log4(z 12) + 1031(3) = 3 8. Consider f(a:) : 41+] 3. Answer the quwtions about this function. (8.1) (3 points) State the equation of the asymp- Answer: tote. (8.2) (6 points) Graph the function and its asymp- tote. Show two points the function goes through and label them with their coordi- nates. (A space for work is also provided here. See comments in previous problem.) 9. Consider an) : log2(:r + 2). Answer the qutions about this function. (9.1) (3 points) State the equation of the asymp- Answer: tote. (9.2) (2 points) State the domain. Answer: (9.3) (6 points) Graph the function and its asymp- tote. Show two points with INTEGER co ordinates that the function gem through and label them with their coordinates. (A space for work is provided. You can make a table if it helps. It is not required, but we will con- sider it for partial credit if there are errors in the graph.)