Question

Question 3 Not yet answered Marked out of 4.00 A company manufactures products A, B and C. Each product is processed in three departments I, II and III. The total available labour-hours per week for departments I, II and III are 900, 1080 and 840, respectively. The time required (in hours per unit) and profit per unit for each product are as follows: 1 A B C 2 2 II 3 2 2 2 1 Profit $ 18 $ 12 $15 1 Formulate a linear programming problem to find the number of units of each product the company should produce to maximise its profit. The application doesn't support attaching files to

Answer 1

Let's assume

number of units of type-A =x

number of units of type-B =y

number of units of type-C =z

now, we can set up system of equations

$2x+1y+2z=900$

3.0 + ly + 2z = 1080

$2x+2y+1z=840$

we can solve for x, y and z

so, we get

$x=180,y=140,z=200$

Quantities:

number of units of type-A =180

number of units of type-B =140

number of units of type-C =200

Maximum Profit:

$Z=18x+12y+15z$

we can plug

$x=180,y=140,z=200$

$Z=18(180)+12(140)+15(200)$

$Z=7920$............Answer