Math

Assignment 1

Kim Davis has decided to purchase a cellular phone, but she is unsure about which rate plan to select. The "regular" plan charges a fixed fee of $55 per month for 1,000 minutes of airtime plus $0.33 per minute for any time over 1,000 minutes. The "executive" plan charges a fixed fee of $100 per month for 1,200 minutes of airtime plus $0.25 per minute over 1,200 minutes.

a.) If Kim expects to use the phone for 21 hours per month, which plan should she select?

b.)At what level of use would Kim be indifferent between the two plans?

Assignment 2

1. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing on line 1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit.

a) Formulate a linear programming model for this problem.

b) Solve this model by using graphical analysis.

Decision variables:  Let x number of Product and y number of Product 2 be produced.

The objective function is: Maximize z = 6x + 4y

Subject to the constraints: 10x + 10y ≤ 100 (Processing time on Line 1 constraint)

7x + 3y ≤ 42 (Processing time on Line 2 constraint)

x ≥ 0 and y ≥ 0

We see that the maximum value of z is $46 and occurs when x = 3 and y = 7

The optimum solution is Product 1 = 3 units and Product 2 = 7 units.

The maximum profit is $46.