Economics question

Peter the Pieman has three delivery vans, V1, V2 and V3, each of which can transport three types of pies, apple pies (A), banana pies (B), and cherry pies (C). Pies are carried in trays of 20. Matrix D shows the numbers of trays of each type of pie the vans can carry simultaneously. Assume vans are full when they start their delivery. A B c v1 15 5 10 0: v2 10 1o 20 v3 10 1o 10 (a) Peter supplies pies to retail shops in two towns, Sunshine (S) and Golden Beach (GB) using his three delivery vans. The number of deliveries each van makes each week to Sunshine and Golden Beach respectively is T1 = (10,15), T2 = (30,10) and T3 = (20,1 0). Formulate this information as a matrix, T, and use matrix multiplication to calculate the number of each type of pie delivered to Sunshine and Golden Beach each week. [Show your answer in matrix form with the rows and columns appropriately labelled. Show all steps of your working clearly.] How many banana pies are delivered to Golden Beach each week? (6 marks) (b) The drivers of the vans collect payment from the shops when they make a delivery. The revenue each van driver receives per delivery is given in matrix R. $ per van r1 2075 R = r2 = 2650 r3 2000 Expressing the problem in matrix format, determine the price Peter charges for each type of pie. Use the adjoint method for nding the inverse of a matrix and show a_|| steps of your working clearly. (14marks)