Hi,

I would like to put this non-linear programming problem into an Excel solver format. The objective is to minimize cost, but also find out what wage is paid at each level of sales:

Sales Level	$0	$5,000	$50,000
Wage Paid	?	?	?

I have attached the problem and the NLP equation. The price is very negotiable, please let me know ti you can help. Thanks!

Problem 3 (5 marks) A salesperson for Fuller Brush has three options: quit, put forth a low-eort level, or put forth a high-eort level. Suppose for simplicity that each salesperson will either sell $0, $5000, or $50000 worth of brushes. The probability of each sales amount depends on the eort level in the manner described in the following table. Eort Low 0.6 0.3 0.1 Size of Sale $0 $5000 $50000 Level High 0.3 0.2 0.5 If the salesperson is paid $w, he or she earns a benet w1/2 . Low eort costs the salesperson 0 benet units while high eort costs 50 benet units. If the salesperson were to quit Fuller and work elsewhere he or she could earn a benet of 20. Fuller wants all salespeople to put forth a high-eort level. The question is how to minimize the cost of doing it. The company cannot observe the level of eort put forth by a salesperson, but they can observe the size of his or her sale. Thus, the wage is completely determined by the size of the sale. Fuller must then determine w0 = wage paid for $0 in sale, w5 = wage paid for $5000 in sales, and w50 = wage paid for $50000 in sales. These wages must be set so that the salespeople value the expected benet from high eort more than quitting and more than low eort. Formulate an NLP that can be used to ensure that all salespeople put forth high eort. (This problem is an example of agency theory.) Solution Decision variables. Let w0 , w5 and w50 represent the wage paid by Fuller Brush to a salesperson if the size of sales is $0, $5000 and $50000, respectively. Objective function. The expected cost associated with a salesperson who puts forth a high-eort level is 0.3w0 + 0.2w5 + 0.5w50 Fuller Brush wants to minimize this cost; therefore, the objective function is min z = 0.3w0 + 0.2w5 + 0.5w50 Constraints. The expected benets for a salesperson who puts forth a high-eort level is 1/2 0.3w0 1/2 + 0.2w5 1/2 + 0.5w50 50 while low-eort level earns expected benets of 1/2 0.6w0 1/2 + 0.3w5 1/2 + 0.1w50 0 To ensure that salespeople value the expected benet from high eort more than quitting and more than low eort, we need, respectively, 1/2 0.3w0 1/2 0.3w0 1/2 + 0.2w5 1/2 + 0.2w5 1/2 1/2 + 0.5w50 50 20 1/2 + 0.5w50 50 0.6w0 1/2 + 0.3w5 1/2 + 0.1w50 To summarize, the NLP is: min z = 0.3w0 + 0.2w5 + 0.5w50 1/2 1/2 1/2 s.t. 0.3w0 + 0.2w5 + 0.5w50 70 1/2 1/2 1/2 0.3w0 0.1w5 + 0.4w50 50 w0 , w5 , w50 0