The Office of Student Affairs provides you with $1,000 to create facemasks that have the slogan "Fletcher Strong." You are given a list of both arizona students and Tufts undergraduates who can do work for you. (situation) To become popular with your Fletcher classmates, you will pay them $20 per hour. You care less about your relationship with Tufts undergraduates, so you pay them $10 per hour. The "production function" for assembling gifts is M= ^F ^T

where M is the number of facemasks, F is the number of hours worked by Fletcher students and T is the number of hours worked by Tufts undergraduates.

i) Use calculus to show that the production function is increasing in F.

ii) Use calculus to show that the production function exhibits diminishing marginal returns in T (hint: this requires the use of the second derivative).

iii) Use calculus to show how the marginal response of the output of M to an increase in T changes with larger values of F (hint: this requires the use of the cross partial derivative).

iv) What is the equation describing the budget constraint for hiring Fletcher students and Tufts undergrads, given the budget of $1,000? Use this equation, along with the production function, to determine the optimal values of F and T.

please help and guide how to solve these quetions