Happy Kid Toy Company produces two types of toy cars, A and B. The company makes RM 50 profit for each toy car of type A and RM 30 profit for each toy car of type B. It takes 4 hours to produce the parts of one unit of A, 2.5 hours to assemble and 1.5 hours to paint. It takes 2 hours to produce the parts of one unit of B, 1 hour to assemble and 2 hours to paint. Every month, 2000 hours are available for pruducing the parts, 1800 hvurs for assembling the parts and 1550 hours for painting the toy cars. The company wishes to determine the best possible combination of toy cars A and B to be produced monthly to maximise the total profit. (i) Formulate the above as a linear programming problem. (ii) Solve the problem graphically. Obtain the optimal product mix and calculate the maximum total profit. (iii) By how much could the unit profit of toy car B change before the optimal product mix could change?

A bacteria culture initially contains 2000 bacteria and doubles every half hour. Find the size of the baterial population after 80 minutes. Find the size of the baterial population after 4 hours.

An apple farm yields an average of 45 bushels of apples per tree when 21 trees are planted on an acre of ground. Each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. How many trees should be planted on an acre in order to get the highest yield? In order to get the highest yield, trees should be planted on an acre. OCEED

A robot manufacturer must produce a total of 1260 robots in one week, including both “building robots”and “destroying robots.” The number of building robots needs to be 3.5 times the number of destroyingrobots. How many of each should they make?

A company produces widgets at plants 1 and 2. It costs 125x1y2 dollars to produce x units at plant 1 and 235x1y3 dollars to produce x units at plant 2.Each plant can produce up to 500 units. Each unit produced can be sold for $10. At most 800 widgets can be sold. Determine how -the company canmaximize its profit.

Two classmates have decided to read all the volumes in a popular series of books. Mia has already read 12 volumes and will continue to read new ones at a rate of 1 volume per week. Beth, who hasn't started reading the series yet, will read 4 volumes per week. At some point, Beth will catch up with Mia and they will be reading the same book. How long will that take? How many volumes will each girl have read by then? In ? weeks, the girls will each have read ? volumes in the series.

Jean typically takes 2 less hours than Donald to assemble a bicycle if each works alone. Jean and Donald worked together to assemble a bicycle for 1 hour, and then Donald finished the job without Jean after an additional 1 hour. How long would it have taken Donald to assemble the bicycle alone? Do not include the units in your answer.

Bottled water and medical supplies are to be shipped to survivors ofan earthquake by plane. Each container of bottled water will serve 10 people and eachmedical kit will aid 6 people. Each plane can carry no more than 80,000 pounds. The bottledwater weighs 20 pounds per container and each medical kit weighs 10 pounds. Each planecan carry a total volume of supplies that does not exceed 6000 cubic feet. Each waterbottle is 1 cubic foot and each medical kit also has a volume of 1 cubic foot.   Thus, the maximum value of z is 36000 and this occurs when x = 0and y = 6000.In practical terms, this means that the maximum number of earthquake survivors whocan be helped with each plane shipment is 36000. This can be accomplished bysending 6000 medical kits.A) TrueB) False

The workers of the company "Malova" work in a 5-day work week and worked them for 22 days in the month of November 2020. The standard work schedule is 8 hours per day with a 30-minute break included in this time. Now, "Malova's" company is in the process of manufacturing screwdrivers and manufactured 3100 pieces of screwdrivers. In addition, the company manufactures screwdrivers in batches of 300 and after each batch makes a pause to check the quality of production and make certain adjustments to the machines if necessary. The break is 1 hour. Calculate the parts produced per hour by the Malova company in November.   Important: Use the formula (the one I put in the image)

the time to assemble a television at a factory is 10 hours. a stereo requires 6 hours. the factory workers can supply at least 2000 and at more 2725 hours of assembly time each week. when the factory is producing 4 times as many televisions as stereos, how many stereos can be manufactured in a week? assume the company cannot produce a fraction of a stereo or television.