Best buy within a budget

Two stock transactions on three days ●○○○○ 10 ptsThe price of a stock on days 1, 2 and 3 is $2, $4 and $1. You may complete at most 2 transactions (a transaction is one buy followed by one sell), and you must sell the stock before you buy again. Find the maximum profit in dollars.
Largest number of jogs ●●○○○ 20 ptsBill can buy jags, jigs and jogs for $1, $2 and $7 each, respectively. What is the largest number of jogs he can purchase if he must buy at least one of each item and will spend exactly $50?
Largest component reliability under budget ●●○○○ 20 ptsA component's cost is $C = (10P)^2$ dollars, where $P$ is the probability that the component operates as expected. A system has two identical components, and both must operate for the system to operate. A total of $173 can be spent on the two components. What is the largest component probability $P$ that can be achieved? Round to two decimal places.
Trash can unit prices and minimum type A quantity ●●○○○ 20 ptsA community buys two models of trash cans, A and B. Buying 3 type-A and 4 type-B cans costs a total of $580, and buying 6 type-A and 5 type-B cans costs a total of $860. (1) Find the unit price of a type-A can and of a type-B can. (2) A total of 200 cans of types A and B are needed, and the total cost must not exceed $15000. What is the least number of type-A cans that should be purchased?
Camel banana relay to market ●●●○○ 50 ptsCorey the Camel harvests 3,000 bananas in her grove. The market is 1,000 miles away. Corey walks to the market and eats one banana for each mile she walks. She can carry at most 1,000 bananas at a time, and she may stash bananas along the route and pick them up on later trips. Find the maximum number of bananas that can reach the market. Round to two decimal places.
Optimal bid for an object ●●●○○ 50 ptsThe owner's value $V$ of an object is uniformly distributed on $[0, 100]$ dollars, and its value to you is $1.8V$ . You make one sealed bid of $b$ dollars. If $b$ is more than the owner's value, he sells it to you and you pay $b$ ; otherwise you get nothing. Choose $b$ to maximise your expected profit. What bid $b$ (in dollars) should you make?
Maximum pencils with cashback ●●●○○ 50 ptsVasya's mother gave him exactly enough money to buy 30 pencils. All pencils cost the same. A store promotion works as follows: for a receipt for a set of 20 pencils, the factory returns 25% of the set's cost, and for a receipt for a set of 5 pencils, it returns 10% of the set's cost. The refunds can be spent on further purchases. What is the maximum number of pencils Vasya can buy?
Elephant carrying bananas to city B ●●●●○ 100 ptsTwo cities $A$ and $B$ are $1000$ km apart. City $A$ has $3000$ bananas and an elephant that can carry at most $1000$ bananas at a time. The elephant eats one banana per km and cannot travel without bananas. Assume the elephant eats continuously, so it can eat fractions of a banana along the way. What is the maximum number of bananas that can be transferred to city $B$ ? Round to two decimal places.

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Bulk discounts and tiered pricing Coin combinations Exchange rates with made-up units Fares and per-mile costs Fees and break-even counts Hourly pay Income and savings Linear cost models Money spent and left Prices from two purchases Purchases with several unknowns Revenue from stock Sales tax and tips Simple purchases Stamps and postage Ticket sales and admissions Unit cost of food and drink Unit prices of pens and pencils