Question

43.

a.

Finance- Allocation of Funds Madison Finance has a total of $20 million earmarked for homeowner and auto loans. On the average, homeowner loans have a 10% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to four times the total amount of automobile loans. Determine the total amount of loans of each type Madison should extend to each category in order to maximize its returns?

Let h = the amount of $$ earmarked for homeowner loans, and
Let a = the amount of $$ earmarked for auto loans

Which option (a, b, c, or d) shows the correct objective function and constraints for this application?

		Objective Function: Maximize Returns, R = 12%*h + 10%*a Constraints: h + a = 20,000,000, 4h >= a, h>= 0, a >= 0
		Objective Function: Maximize Returns, R = 10%*h + 12%*a Constraints: h + a = 20,000,000, h >= 4a, h>= 0, a >= 0
		Objective Function: Maximize Returns, R = 10%*h + 12%*a Constraints: h + a = 20,000,000, 4h >= a, h>= 0, a >= 0
		Objective Function: Maximize Returns, R = 12%*h + 10%*a Constraints: h + a = 20,000,000, h >= 4a, h>= 0, a >= 0

b.

Manufacturing-Production Scheduling An acoustical company manufactures a CD storage cabinet that can be bought fully assembled or as a kit. Each cabinet is processed in the fabrications department and the assembly department. If the fabrication department only manufactures fully assembled cabinets, then it can produce 200 units/day; but if it only manufactures kits, then it can produce 300 units/day. Each fully assembled cabinet contributes $40 of profit, while each cabinet kit contributes $50 of profit. How many fully assembled units and contributes $40 of profit, while each cabinet kit contributes $50 of profit. How many fully assembled units and how many kits should the company produce per day in order to maximize its profits?

Let f = the number of fully assembled cabinets, and
Let k = the number of cabinet kits

Which option (a, b, c, or d) shows the correct objective function and constraints for this application?

		Objective Function: Maximize Profit, P = 40f + 50k Constraints: f <= 200, k <= 300, f>= 0, k >= 0
		Objective Function: Maximize Profit, P = 40f + 50k Constraints: f <= 300, k <= 200, f>= 0, k >= 0
		Objective Function: Maximize Profit, P = 40f + 50k Constraints: f >= 200, k >= 300, f>= 0, k >= 0
		Objective Function: Maximize Profit, P = 50f + 40k Constraints: f >= 200, k <= 300, f>= 0, k >= 0

Answer 1