Question

For the problem below:

"A food company produces two types of turkey cutlets for sale to fast-food restaurants. Each type of cutlet consists of white meat and dark meat. Cutlet 1 sells for $4/lb and must consist of at least 70% white meat. Cutlet 2 sells for $3/lb and must consist of at least 60% white meat. At most 6000 pounds of cutlet 1 and 2000 pounds of cutlet 2 can be sold. The two typesof turkey used to manufacture the cutlets are purchased from a turkey farm. Each type 1 turkey costs $10 and yields 5 lbs of white meat and 2 lbs of dark meat. Each type 2 turkey costs $8 and yields 3 lbs of white meat and 3 lbs of dark meat. Determine how the company can maximize its profit."

I get final answer as 18710. Is that correct?

Answer 1

Decision variables

xi= number of turkeys of type i to buy,i= 1,2

yjk= pounds of meat type j used to make cutlet k, k= 1,2, let j= 1,2 represent white,dark

Objective Function to maximize profit

Profit= Sales revenue- Cost

maximize 4(y11+y21) + 3(y12+y22)-10x1-8x2

Constraints

The white meat content in x1 turey is 5 and in x2 turkey is 3

The meat type 1 used in cutlet 1 and meat type 1 in cutlet 2 sums should be less than or equal to the total white meat content

y11+y12≤5x1+ 3x2

For dark meat similarly

y21+y22≤2x1+ 3x2

Cutlet 1 should have 70% of white meat

y11≥.7(y11+y21)

Cutlet 2 should contain 60% of white meat

y12>=0.6(y12+y22)

At most 6000 lbs of cutlet 1 to be sold

y11+y21<=6000

similarly,

y12+y22<=2000

xi,yjk>=0

Simplifying the constraints

LP becomes

Maximize 4(y11+y21) + 3(y12+y22)-10x1-8x2

Subject to

y11+y12-5x1- 3x2<=0

y21+y22-2x1- 3x2<=0

0.3y11-0.7y21>=0

0.4y12-0.6y22>=0

y11+y21<=6000

y12+y22<=2000

Solving in solver

The total profit I got is 18571.42 if I am not constraining to integer values

Please comment if any doubt

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