Linear Programming

Good day sir.
I particularly have a challenge with the (d) section, where it states… and if so STATE HOW MANY OVERTIME HOURS SHOULD BE WORKED?

Allen Ltd. Makes two products A and B. Standard revenues and costs per unit for these products are shown below: Selling Price (A)200 (B)180
Variable costs: Material X ($10 per kg) (A)40 (B)40
Direct labour ($8 per hour) (A)32 (B)16 Plating ($12 per hour) (A)12 (B)24 Other variable costs (A)76 (B)70
Contribution (A)40 (B)30
Fixed overheads (allocated at $7 per direct labour hour (A)28 (B)14 Standard profit per unit (A)12 (B)16 In any week the maximum availability of inputs is limited to the following: Material X 120 kg Direct Labour 100 hours Planting Time 50 hours. A management meeting recently considered ways of increasing the productivity of the department. It was decided that each of the following possible changes to the existing situation should be examined independently of each other: 1. A new product C sold at $240 per unit. Each unit would require the following: Material X 5kg Direct labour 5 hours Planting Time 1 hour Other variable costs $90 2. Overtime could be introduced and would be paid at a premium of 50% above normal rates. Requirements: a. Formulate a linear programme to determine the production policy which maximeses the profit of Ade Ltd. In the present situation (i.e ignoring the alternative assumptions in 1 and 2 above). Solve and specify the optimal product mix and weekly profit. b. Calculate the shadow prices of the constraints c. Using shadow prices (dual values), ascertain whether product C would be a profitable addition to the product range. d. Ignoring the possibility of extending the product range, determine whether overtime working would be worthwhile, and if so state how many overtime hours should be worked