Question

Sun Systems makes two types of retractable awnings - Premium and Deluxe. Each Premium unit produced requires 50 minutes processing on Machine 1 and 30 minutes processing on Machine 2. Each Deluxe unit produced requires 25 minutes processing on Machine 1 and 30 minutes processing on Machine 2. At the start of the current week there are 25 Premium units and 40 Deluxe units in stock. Machine 1 has 20 hours of processing time available during the current week and Machine 2 has 15 hours of processing time available during the current week. The demand for Premium units in the current week is forecast to be 40 units and for Deluxe units is forecast to be 50 units.

How many Premium units and how many Deluxe units should be made during the current week to maximize the sum of the Premium units and Deluxe units in stock at the end of the current week?

If multiple solutions (optima) exist, you must find them ALL to receive full credit.

Hint: Will the method of solution you choose be able to find multiple optima?

Answer 1

answer:

• Let the quantity of premium units made amid the week be 'P' and number of luxurious units made be 'D'.
• Whole of shutting stock = aggregate of opening stock + P + D - entirety of week after week request = (25+40)+P+D-(40+50) = P+D-25
• This is the target capacity and this must be expanded.

Constraints:

(I) 50P+25D<=1200. This limitation is identified with machine 1. The aggregate of time required by Premium and fancy ought not surpass the accessible time. Accessible time = 20 hours or 20*60 = 1200 minutes.

(ii) 30P+30d<=900. This limitation is identified with machine 2. The aggregate of time required by Premium and fancy ought not surpass the accessible time. Accessible time = 15 hours or 15*60 = 900 minutes.

(iii) P,D>=0. This is non negative limitation i.e. generation can't be a negative number.

• Understanding in exceed expectations, utilizing the solver work, following arrangement is gotten:

• so these is the total explanation of above