Question

you are in charge of the annual charity fundraiser sponsored by your company. what is the minimum amount of money the charity would receive given these factors? the company has guaranteed an arrangement of at least 1000. they company has guaranteed total ticket receipts of at least $4800. the tickets are $4 for employees and $6 for nonemployees. the charity will receive $2.50 for every employee ticket and $4.50 for every nonemployee ticket. Solve this problem and graph it using the linear method of optimization.

Answer 1

Let there be x employees and y non-employees and z is the amount of money charity would receive.

Then, the linear programming problem is :

Minimize z = 2.5x+4.5y

Subject to x+y 1000

4x+6y 4800

x, y 0

We consider the inequalities as equations and plot them.

Here, the region is unbounded above.

The corner points are A(0,1000), B(600,400), C(1200,0).

Now, the values of the objective function :

z_A = 2.5*0+4.5*1000 = 4500

z_B = 2.5*600+4.5*400 = 3300

z_C = 2.5*1200+4.5*0 = 3000

Therefore, z_min = 3000 at x = 1200, y = 0

Hence, the minimum amount of money the charity would receive is $3000.