4.21 Problem Hints
1) The company needs to know the following: How many gloves of each type to make (3 variables) How many full-timers, and how many part-times to hire (2 variables) Therefore we will need 5 decision variables. Remember, the variables don't need to be the same `kind' of thing. They are just unknown quantities. 2) The Objective Function needs to be something to maximize or minimize: Since they seem to be giving us the unit profit per glove, the Objective Function could be the Total (Net) Profit. (see italics in the problem description). 3) You now have to think what `contributes' to the Net Profit (remember Unit Contribution?) The gloves produced (and sold) contribute but positively, how about the people hired? What is their `contribution'? Wouldn't they be contributing (negatively) their cost? But what's the unit cost? We need to get everything to a common unit so we don't deal with apples and oranges. How about the cost per week? Then the number of gloves produced would be weekly production numbers. 4) What are the constraints? Leather, labor hours, minimum number of full-timers, and the ratio of full-times to part-timers (like problem 4.14). The `tricky' one is labor hours. But remember: the labor hours required to make the gloves must be provided by the people they hire. Also remember we decided to use a week as unit of time.