PLEASE ANSWER WITH EXCEL REPORT AND SHOW HOW TO GET THE ANSWER AND SENSITIVITY REPORTS.

Q1. 20 points Uggo makes sweaters and vests by combining labor and yarn. For each period Uggo only has 40 hours of labor and has a total of 120 pounds of yarn to use on these two products. Each sweater takes 1 hour and 4 pounds of yarn, while a vest requires 2 hours and 3 pounds of yarn. Uggo would like to earn as much profit as possible. Initially, Uggo believes it can earn $40 profit per sweater and $50 profit per vest. Confirm Uggo believes it should make 24 sweaters and 8 vests by formulating a linear program for the problem where you will include with your answer an Excel file including both an answer and sensitivity report.

On the sensitivity report, where do you look to find out if an additional hour of labor over 40 hours would be useful to the firm? \

What do you conclude about the usefulness of an additional hour of labor?

Uggo has found it is not selling 24 sweaters and 8 vests per period. You explain that their formulation of profit as linear is probably not appropriate. One idea for this is that the level of sweaters and vests desired likely depends on the demand for each and these demands treat the price and quantity demand as inversely related.

Say the firm believes the demand for sweaters and vests and costs are Sweater demand S = 120 2Ps and cost 20S, where S = quantity of sweaters and Ps = price of sweaters, and Vest demand V = 180 3Pv and cost 10V, where V = quantity of vests and Ps = price of vests.

Now formulate this problem as a nonlinear programming problem in Excel and include an Answer report with your work.

How many sweaters and how many vests should it now make to maximize profit? Does the firm have any use for an additional pound of yarn at this optimal solution and explain how you know this?