I need help creating the constraints.
Quick-Screen is a clothing manufacturing company that specializes in producing commemorative shirts immediately following major sporting events such as the World Series, Super Bowl, and Final Four. The company has been contracted to produce a standard set of shirts for the winning team, either State University or Tech, following a college football bowl game on New Year’s Day. The items produced include two sweatshirts, one with silk-screen printing on the front and one with print on both sides, and two T-shirts of the same configuration (i.e. one with front only print and the other with print on both sides). The company has to complete all production within 72 hours after the game, at which time a trailer truck will pick up the shirts. The truck has enough capacity to accommodate 1,200 standard-size boxes. A standard-size box holds 12 T-shirts. A box of 12 sweatshirts is three times the size of a standard box. The company has budgeted $25,000 for the production run. It has 500 dozen blank sweatshirts and T-shirts each in stock, ready for production.
• sf = number of units of Sweatshirt – Front to produce
• sb = number of units of Sweatshirt – Back to produce
• tf = number of units of T-Shirt – Front to produce
• tb = number of units of T-Shirt – Both Sides to produce
Constraints (so far what i have done)
1. $.10Xsf + .25Xsb + .08Xtf + .21Xtb ≤ 72 hours (Production hours)
2. $36Xsf + $48Xsb + $25Xtf + $35Xtb ≤ $25,000 (Production cost)
3. Xtf + Xtb + 3(Xsf+Xsb) ≤ 1200 boxes (Total capacity in truck)
4. Xsf + Xsb ≤ 500 (Available sweatshirts)
5. Xtf + Xtb ≤ 500 (Available t-shirts)
6. Xsf + Xsb + Xtf + Xtb ≥ 0 (non-negativity condition)
Is this correct??
On 1, you have a production time constraint equalling cost on the left, that makes no sense.
On 2, Itlooks right, but I cant verify the unit costs.
On 3,4,5,6 they are correct.
Your constraints look mostly correct, but there are a few adjustments that could be made for clarity and accuracy:
1. Production hours constraint: This constraint should specify the number of units produced, not the number of production hours. Assuming that each unit takes a fixed amount of time to produce, you need to multiply the number of units by the time it takes to produce each unit. Here's the revised constraint:
0.10Xsf + 0.25Xsb + 0.08Xtf + 0.21Xtb ≤ 72 * (Xsf + Xsb + Xtf + Xtb), where Xsf, Xsb, Xtf, and Xtb represent the number of units produced.
2. Production cost constraint: This constraint should also specify the number of units produced:
36Xsf + 48Xsb + 25Xtf + 35Xtb ≤ $25,000
3. Total capacity in the truck: This constraint seems to be correct, assuming that all the boxes are of the same size and there is no need to consider the size of the sweatshirt boxes separately. However, it is not clear how many items fit in a box. Based on the information given, it seems like a standard-size box holds 12 T-shirts, but there is no indication of how many sweatshirts can fit in a box. If it is not specified, you may assume that the capacity constraint refers only to T-shirts:
Xtf + Xtb ≤ 1200 * 12
4. Available sweatshirts and T-shirts: These constraints seem to be correct, assuming that "500 dozen" means 500 * 12 = 6,000 items:
Xsf + Xsb ≤ 6,000
Xtf + Xtb ≤ 6,000
5. Non-negativity condition: This constraint is correct as it is:
Xsf, Xsb, Xtf, Xtb ≥ 0
Make sure to review these adjustments and clarify any necessary information before implementing this formulation.