Harrington Corporation produces three products, A, B, and C. Pertinent information on these products is as follows: ProductSelling Price per UnitVariable Cost per UnitFixed Costper UnitDL Hoursper UnitA (Anchor bolts)$4.00 $1.00 $2.00 2 B (Bearings)$3.50 $0.50 $2.00 2 C (Castings)$6.00 $2.00 $3.00 3 There are 150 direct labor hours available. Machine-hour capacity allows 100 anchor bolts, only; 50 bearings, only; 40 casters, only; or any combination of the three that does not exceed the capacity. The direct labor hour constraint for Harrington's linear programming model is:

Labour hours constraint :  2a + 2b + 3c ≤ 150

Explanation:

Linear programming is a mathematical model that is used to solve a problem when a firm wants to maximize profit in the midst of multiple resource constraints.

The following steps should be followed:

Step 1: Define the variables

a= the units of product Anchor

b=  the units of product Bearing

c= the units of product Casting

Step 2: Define the constraints:

The constraints represent the limitations which could be resource; in this case machine hours and direct labour hours. Since the constraint in focus is labour hours , so we only consider it.

Subject

Constraints:  Labour hours : 2a + 2b + 3c ≤ 150

Non-negativity constraints a, b , c ≥ 0

Since the total available labour hours is 150 hours then the total consumption hours can either be equal to or less than 150, but can never be higher than 150.

The labour hours constraint  is represented by 2a + 2b + 3c ≤ 150

answer; (15,000)workers each