Exercise 6.2

19. Manufacturing A company manufactures two types of leaf blowers, an electric Turbo model and gas powdered Tornado model. The company’s production plan calls foe the production of at least 780 blowers per month. It costs $78 to produce each Turbo model and $117 to manufacture each Tornado model, and the company has at most $76,050 per month to use for the production. Find the number of units that should be produced to maximize the profit for the company if the profit on each Turbo model is $32 and the profit on each Tornado model is $45.

21. Manufacturing Safeco Company produces two types of chainsaws, the Safe cut and the Safe cut Deluxe. The Safe cut model requires 2 hours to assemble and 1 hour to paint, and the Deluxe model requires 3 hours to assemble and ½ hour to paint. The daily maximum numbers of hours available for assembly is 36, and the daily maximum number of hours available for painting is 12. If the profit is $24 per units on the safe cut model and $30 per units per the Deluxe model, how many units of each type will maximum the daily profit?

25. Production A firm produces three different-size television sets on two assembly lines. The following table summaries the production capacity of each assembly line, the number of each size TV ordered by a retailer, and the daily operating costs for each assembly line. How many days should each assembly line run to fill this order with minimum cost? What is the minimum cost?


Assembly   Line 1

Assembly   Line 1

Number   Ordered



80   per day

40   per day




20   per day

20   per day




100   per day

40   per day



Daily   Cost($)



31. Nutrition In a war hospital, patients are grouped into two general nutritional categories depending on the amount of solid food in their diet, and are provided two different diets with different amounts of the solid foods and with some detrimental substances. Table below gives the patients groups, the weekly diet requirements for each group, ant the amount of detrimental substance in each diet. How many serving of each diet will satisfy the nutritional requirements and minimize the detrimental substance? What is the minimum amount of detrimental substance?


Diet   A (oz/serving)

Diet   B (oz/serving)

Minimum   Daily requirement (oz)


Group   1





Group   2