Please provide answers in these steps1Define the variables 2

Please provide answers in these steps:1-Define the variables 2- Provide formulas for objective function 3- State Constraints. 4.) Provide the T,C/C,P. You are not solving the problem

Katilin Incorporated manufacturers blue jeans. Three brands are considered: A, B, and C. The manufacture of brand A requires 2 minutes machine time, 30 minutes labor, and costs $7. Brand B requires 2.5 minutes machine time, 40 minutes labor and costs $10 to produce. Finally, brand C, the top of the line, requires 3 minutes machine time, 1 hour labor and costs $13 to produce. Brand A sells for $12, brand B for $14, and brand C for $20.

The company works on a weekly schedule of five days, with two shifts of 7.5 hours (net time) each. It has four machines available for production and 50 employees on each shift. Its weekly manufacturing budget is $10,000. Its declared objective is profit maximization.

Solution

1. The variables will be the number of units of Brand A,B,C to be manufactured. Let x,y,z be the number of units of Brand A,B,C to be manufactured respectively.

2. The objective is profit maximization. Profit = revenues - costs. total revenue = revenue per unit*no. of units sold. total costs = cost per unit*no. of units sold

A: revenue = 12x. cost = 7x. profit = 12x - 7x = 5x

B: revenue = 14y. cost = 10y. profit = 14y - 10y = 4y

C: revenue = 20Z. cost = 13z. profit = 20z - 13z = 7z

The objective function that is to be maximized is 5x+4y+7z

3. Constraints:

a. . weekly hours available = 50 (no. of employees on each shift) *7.5 (net time) *2 (no. of shifts) *5 days= 3750 hours or 3750*60 = 225,000 minutes

the first constraint is that total labor hours should not exceed 4500 minutes i.e 30x+40y+60z<=225,000

b. availabel machine hours = 4 machines * 7.5 hours*2 shifts *5 days = 300 hours or 300*60 = 18,000 minutes

so, 2x+2.5y+3z<=18,000

c. manufacturing budget is 10,000

so, 7x+10y+13z<=10,000

d. production cannot be negative, so the last constraint will be:

x,y,z>=0