Q1:

Import Motors imports the fully assembled cabs and chassis for a line of small trucks. They fabricate the beds for these trucks and mount the beds on the cab and chassis. The finished trucks are shipped to dealers. Their full cost of fabricating a bed is £220, and their cost of a cab and chassis is £2000. The final assembly of bed to cab and chassis cannot take place if they are short of either one. Cabs and chassis or beds that cannot be matched are stored in their back lot at an inventory cost of 1% (of unit cost) per week. They can produce 1000 beds per week and have the following cab and chassis arrivals scheduled over the next month:

Week Cab and Chassis
1 1500
2 0
3 1700
4 0

If they currently have nothing stored in the back lot, and if items produced and delivered in the same week incur no inventory cost, how many beds should they produce each week to minimize total four week inventory cost?

Q2:

Same as in part (a) Q3, except that the trucks were in two colours: red and blue. Naturally, the colour of the bed must be the same as the cab and the chassis. The new details about the next month's scheduled arrivals are as follows:
Week Cab & Chassis______
Red Blue_____
1 1000 500
2 0.0 0.0
3 100 1600
4 0 0

How many beds should they produce each week to minimize total four week inventory cost?

Q3:

Same as in part (b) Q3, except that all the blue trucks are in great demand. Therefore management wants all blue trucks to be shipped in the same week that the cab and chassis arrive in the port. How many beds should they produce each week to minimize total four week inventory cost?
(d)
Same as in part (b) Q3, except that their bed production plant is set up to produce beds in 100 bed lots. How many beds should they produce each week to minimize total four week inventory cost?