A factory produces three types of widgets P, Q and R. In a particular week, the cost of producing a batch of each widget type is recorded as follows:
• Producing 3 batches of P, 2 batches of Q and 1 batch of R costs ₹52,000.
• Producing 2 batches of P, 3 batches of Q and 2 batches of R costs ₹60,000.
• Producing 1 batch of P, 1 batch of Q and 2 batches of R costs ₹38,000.
Assuming the cost per batch of each widget type remains constant throughout the week,
(i) Formulate a system of three linear equations in the unknown costs per batch of widgets P, Q and R.
(ii) Express the system in the compact form AX=B.
(iii) Find the cost per batch of each widget type.
(iv) Using the costs obtained in part (iii), calculate the total cost of producing 5 batches of P, 4 batches of Q and 3 batches of R.