1.A client has come to your investment company with 500,000 to invest. The client has asked that you invest some, or all, of this money in four types of investment in order to maximize his total return (where return is the money made on an investment).

G: Government bonds, producing 8% return per annum

C: Corporate bonds, producing 9% return per annum

S: Shares of companies in the service sector, 10% return per annum

M: Shares of companies in the manufacturing sector, 8% return per annum

The client has asked that:

Corp Bonds: The amount invested in corporate bonds should be at least 10% of the total

Govt Bonds: The amount invested in government bonds should be at least 40% of the total

Manuf Shares: No more than half of the amount invested should be in manufacturing shares

Total Shares: Total shares should be at least half of the amount invested Serv Shares: The amount invested in service company shares should be at least as much as that in manufacturing shares.

1a) Formulate the problem as a linear program, (using G, C, S and M as the variable names), including the objective function and all constraints.