solve the following linear programming model by using Microsoft Excel

min Z= 3x1 + 6x2

subject to 7x1 + 3x2 _>_ 40

x1,x2, _>_ 0 and integer

Each week they have 80 hours of labor and 36 oz. silver available. it takes 8 hours of labor and 2 oz of silver to make a pin and 10 hours of labor and 6 oz. of silver to make a necklace each pin also contains a small gem of some kind. the demand for pin is in no more than six per week. a pin earns the jeweler $400 in profit and a necklace earns $100 the jeweler wants to know how many of each item to make each week to maximize profit

a) formulate an integer programming model for this problem

b) solve the linear programming model that you formulated

c) compare this solution with the solution without integer restriction and indicate whether the rounded-down solution would have been optimal.