Company Efficiency wants to be able to help its citizens with a current crisis it is undergoing but at the same time would like to maximize profit. The current crisis requires that gowns, ventilators and masks are created. There are three private companies that are willing to help with manufacturing these subject to some constraints on labor hours. At Company A the time it requires to make a gown is 1 hour, to make a ventilator is 2 hours, and to make a mask is 3 hours for a maximum total hours not to exceed 10 hours. At Company B, the time it requires to make a gown is 2 hours, to make a ventilator is 1 hour, and to make a mask is also 1 hour, for a maximum total hours not to exceed 8 hours.
At Company C, the time it requires to make a gown is 3 hours, to make a ventilator is 0 hours (they seemed to have stocked up on these), and to make a mask is 4hours, for a maximum total hours not to exceed 6 hours.
Company Efficiency is willing to work with these companies to help society but also maximize profit; Currently the cost of producing a gown is $1, a ventilator is $5, and a mask is $10. Help Company Efficiency maximize the profit by finding the number of gowns (x1), ventilators(x2), and masks(x3) needed to achieve this.
Show all your work (every step) and if possible see if you could confirm your results in R.