For each of the experiment given below, identify the most appropriate design and its associated statistical model in details:

a) An industrial engineer is interested to study the effect long working hours on the productivity of his staffs. He considers three working durations; 4 hours, 8 hours and 12 hours and measure the output produced by 20 staffs at the end of the identified working duration. The data was recorded during day and night shifts and there are male and female staffs which may contribute possible effect on the productivity.

b) A test engineer would like to study the strain of glass cathode supports on the production machines. For this purpose, she chose 5 production machines. Each machine has 4 components called 'heads' which produces the glass. She took 4 samples of measurement of the strain reading of the glass produced from each head at random and in total, the 80 measurements were collected at random.

c) A food scientist is interested in the production of ice cream. He has two different recipes (A and B). Additional factors that may affect the ice cream are the temperature at which the process is run and the pressure used. He wish to investigate the effects of recipe, temperature, and pressure on ice cream viscosity. The production machinery is available for 8 days, and two batches of ice cream can be made each day. A fresh supply of milk will be used each day, and there is probably some day to day variability in the quality of the milk. The production machinery is such that temperature and pressure have to be set at the start of each day and cannot be changed during the day. Both temperature and pressure can be set at one of two levels (low and high). Each 2 batch of ice cream will be measured for viscosity

please help me answer the questions for experimental of design and analysis course. Thanks