Quantitative techniques

Question

A transporter has two types of trucks to transport sugar. Type A truck carries 2000 bags while Type B carries 3000 bags per trip. The transporter is required to transport 120,000 bags and he has to make no more than 50 trips. In his operations experience, Type B trucks can make at most twice the number of trips Type A makes.

Required:

a) Represent this information as inequalities (2 marks)

b) If the transporter makes a profit of Ksh 10,000/- per trip from Truck Type A and Ksh 20,000/- per trip for Truck Type B, calculate the number of trips he should make so as to maximize his profits. (8 marks)

c) If the transporter was to overhaul his fleet so as to retain only one type of truck, recommend the type to retain giving reasons.

Answer 1

(a)

2,000 A + 3,000 B >= 120,000;

A + B <= 50;

B <= 2A

A >= 0

B >= 0

(b) Profit(A,B) = 10,000 A + 20,000 B

Graphing (a), the feasible solutions are in a shape of triangle. Construct a straight line L: 10,000 A + 20,000 B = 0. Construct L' such that it is parallel to L and move towards the top right corner (which are larger A and B for larger profit). The max profit is located at the intersection of B = 2A and A + B = 50. By solving the simultaneous equations, A = 50/3, B = 100/3. According to B <= 2A, B cannot be more when rounding. So we round down B to 33 and A will be 17. Finally, the max profit is 10,000 (17) + 20,000 (33) = Ksh 830,000.

(c) The transporter should retain Truck type B since it contains more and earns more for each trip.