PLESE using math(and not excel) and by hand solve the following question thank you !

HiFi company produces two models of electronic gadgets that use resistors, capacitors, and chips. The following table summarizes the data of the situation: Unit resource requirement Maximum Resource Model 1 Model 2 availability (units) (units) (units) Resistor Capacitor Chips Unit profit (S) 1200 1000 800 Let xi and x2 be the amounts produced of Models 1 and 2 respectively. Following are the LP model and its associated optimal simplex tableau. maximize Z= 3x1 + 4x2 subject to 2x + 3x2 0 Basic 53 Solution 1750 0 X1 X2 51 52 0 0 5/4 4 1/ 1 0 -1/4 3/4 00- 22 1 1/2 0 450 400 -1/2 100 All questions below should be answered using the information for the optimal solution given in the tableaux above. a) If the available number of resistors is increased to 1300 units, find the new optimal solution. What is the range of bi so that the optimal basis to the original problem remains unchanged? (10 points) b) If the unit profit of Model 1 is increased to $6, while ; = 12 determine the new solution. What is the range of aj so that the optimal basis to the original problem remains unchanged? (10 points) c) If a new constraint, 3x + 4x2 0 Basic 53 Solution 1750 0 X1 X2 51 52 0 0 5/4 4 1/ 1 0 -1/4 3/4 00- 22 1 1/2 0 450 400 -1/2 100 All questions below should be answered using the information for the optimal solution given in the tableaux above. a) If the available number of resistors is increased to 1300 units, find the new optimal solution. What is the range of bi so that the optimal basis to the original problem remains unchanged? (10 points) b) If the unit profit of Model 1 is increased to $6, while ; = 12 determine the new solution. What is the range of aj so that the optimal basis to the original problem remains unchanged? (10 points) c) If a new constraint, 3x + 4x2